Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.35690 | 0.512858 | 0.256429 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256429 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.29590 | 1.59677 | 0.798387 | − | 0.602145i | \(-0.205687\pi\) | ||||
0.798387 | + | 0.602145i | \(0.205687\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35690 | −0.362646 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.04892 | −0.496935 | −0.248468 | − | 0.968640i | \(-0.579927\pi\) | ||||
−0.248468 | + | 0.968640i | \(0.579927\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.24698 | −0.744908 | −0.372454 | − | 0.928051i | \(-0.621484\pi\) | ||||
−0.372454 | + | 0.928051i | \(0.621484\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.35690 | −0.296099 | ||||||||
\(22\) | −5.29590 | −1.12909 | ||||||||
\(23\) | 1.33513 | 0.278393 | 0.139196 | − | 0.990265i | \(-0.455548\pi\) | ||||
0.139196 | + | 0.990265i | \(0.455548\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.35690 | 0.256429 | ||||||||
\(29\) | −5.13706 | −0.953929 | −0.476964 | − | 0.878923i | \(-0.658263\pi\) | ||||
−0.476964 | + | 0.878923i | \(0.658263\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −2.80194 | −0.503243 | −0.251621 | − | 0.967826i | \(-0.580964\pi\) | ||||
−0.251621 | + | 0.967826i | \(0.580964\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.29590 | −0.921897 | ||||||||
\(34\) | 2.04892 | 0.351386 | ||||||||
\(35\) | −1.35690 | −0.229357 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.24698 | 0.369401 | 0.184701 | − | 0.982795i | \(-0.440868\pi\) | ||||
0.184701 | + | 0.982795i | \(0.440868\pi\) | |||||||
\(38\) | 3.24698 | 0.526730 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.6310 | −1.66029 | −0.830143 | − | 0.557550i | \(-0.811742\pi\) | ||||
−0.830143 | + | 0.557550i | \(0.811742\pi\) | |||||||
\(42\) | 1.35690 | 0.209374 | ||||||||
\(43\) | 4.41789 | 0.673723 | 0.336861 | − | 0.941554i | \(-0.390635\pi\) | ||||
0.336861 | + | 0.941554i | \(0.390635\pi\) | |||||||
\(44\) | 5.29590 | 0.798387 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.33513 | −0.196854 | ||||||||
\(47\) | −4.82371 | −0.703610 | −0.351805 | − | 0.936073i | \(-0.614432\pi\) | ||||
−0.351805 | + | 0.936073i | \(0.614432\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.15883 | −0.736976 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.04892 | 0.286906 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.2349 | 1.95531 | 0.977657 | − | 0.210207i | \(-0.0674139\pi\) | ||||
0.977657 | + | 0.210207i | \(0.0674139\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.29590 | −0.714099 | ||||||||
\(56\) | −1.35690 | −0.181323 | ||||||||
\(57\) | 3.24698 | 0.430073 | ||||||||
\(58\) | 5.13706 | 0.674529 | ||||||||
\(59\) | −13.8998 | −1.80960 | −0.904798 | − | 0.425841i | \(-0.859978\pi\) | ||||
−0.904798 | + | 0.425841i | \(0.859978\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −3.62565 | −0.464216 | −0.232108 | − | 0.972690i | \(-0.574562\pi\) | ||||
−0.232108 | + | 0.972690i | \(0.574562\pi\) | |||||||
\(62\) | 2.80194 | 0.355846 | ||||||||
\(63\) | 1.35690 | 0.170953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.29590 | 0.651880 | ||||||||
\(67\) | −9.03684 | −1.10403 | −0.552013 | − | 0.833836i | \(-0.686140\pi\) | ||||
−0.552013 | + | 0.833836i | \(0.686140\pi\) | |||||||
\(68\) | −2.04892 | −0.248468 | ||||||||
\(69\) | −1.33513 | −0.160730 | ||||||||
\(70\) | 1.35690 | 0.162180 | ||||||||
\(71\) | −11.7506 | −1.39454 | −0.697271 | − | 0.716807i | \(-0.745603\pi\) | ||||
−0.697271 | + | 0.716807i | \(0.745603\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.1032 | 1.41657 | 0.708287 | − | 0.705925i | \(-0.249468\pi\) | ||||
0.708287 | + | 0.705925i | \(0.249468\pi\) | |||||||
\(74\) | −2.24698 | −0.261206 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −3.24698 | −0.372454 | ||||||||
\(77\) | 7.18598 | 0.818919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.259061 | 0.0291467 | 0.0145733 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145733 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.6310 | 1.17400 | ||||||||
\(83\) | −3.02177 | −0.331682 | −0.165841 | − | 0.986152i | \(-0.553034\pi\) | ||||
−0.165841 | + | 0.986152i | \(0.553034\pi\) | |||||||
\(84\) | −1.35690 | −0.148049 | ||||||||
\(85\) | 2.04892 | 0.222236 | ||||||||
\(86\) | −4.41789 | −0.476394 | ||||||||
\(87\) | 5.13706 | 0.550751 | ||||||||
\(88\) | −5.29590 | −0.564545 | ||||||||
\(89\) | 5.47650 | 0.580508 | 0.290254 | − | 0.956950i | \(-0.406260\pi\) | ||||
0.290254 | + | 0.956950i | \(0.406260\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.33513 | 0.139196 | ||||||||
\(93\) | 2.80194 | 0.290547 | ||||||||
\(94\) | 4.82371 | 0.497527 | ||||||||
\(95\) | 3.24698 | 0.333133 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.85086 | 0.594064 | 0.297032 | − | 0.954867i | \(-0.404003\pi\) | ||||
0.297032 | + | 0.954867i | \(0.404003\pi\) | |||||||
\(98\) | 5.15883 | 0.521121 | ||||||||
\(99\) | 5.29590 | 0.532258 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.39612 | −0.835446 | −0.417723 | − | 0.908575i | \(-0.637172\pi\) | ||||
−0.417723 | + | 0.908575i | \(0.637172\pi\) | |||||||
\(102\) | −2.04892 | −0.202873 | ||||||||
\(103\) | 13.6353 | 1.34353 | 0.671765 | − | 0.740765i | \(-0.265537\pi\) | ||||
0.671765 | + | 0.740765i | \(0.265537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35690 | 0.132419 | ||||||||
\(106\) | −14.2349 | −1.38262 | ||||||||
\(107\) | 3.92394 | 0.379341 | 0.189671 | − | 0.981848i | \(-0.439258\pi\) | ||||
0.189671 | + | 0.981848i | \(0.439258\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.554958 | 0.0531553 | 0.0265777 | − | 0.999647i | \(-0.491539\pi\) | ||||
0.0265777 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(110\) | 5.29590 | 0.504944 | ||||||||
\(111\) | −2.24698 | −0.213274 | ||||||||
\(112\) | 1.35690 | 0.128215 | ||||||||
\(113\) | 4.39373 | 0.413328 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(114\) | −3.24698 | −0.304108 | ||||||||
\(115\) | −1.33513 | −0.124501 | ||||||||
\(116\) | −5.13706 | −0.476964 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.8998 | 1.27958 | ||||||||
\(119\) | −2.78017 | −0.254858 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 17.0465 | 1.54968 | ||||||||
\(122\) | 3.62565 | 0.328251 | ||||||||
\(123\) | 10.6310 | 0.958567 | ||||||||
\(124\) | −2.80194 | −0.251621 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.35690 | −0.120882 | ||||||||
\(127\) | −2.23490 | −0.198315 | −0.0991576 | − | 0.995072i | \(-0.531615\pi\) | ||||
−0.0991576 | + | 0.995072i | \(0.531615\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.41789 | −0.388974 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.51573 | −0.744023 | −0.372011 | − | 0.928228i | \(-0.621332\pi\) | ||||
−0.372011 | + | 0.928228i | \(0.621332\pi\) | |||||||
\(132\) | −5.29590 | −0.460949 | ||||||||
\(133\) | −4.40581 | −0.382032 | ||||||||
\(134\) | 9.03684 | 0.780664 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 2.04892 | 0.175693 | ||||||||
\(137\) | −13.1685 | −1.12506 | −0.562531 | − | 0.826776i | \(-0.690172\pi\) | ||||
−0.562531 | + | 0.826776i | \(0.690172\pi\) | |||||||
\(138\) | 1.33513 | 0.113653 | ||||||||
\(139\) | 7.17629 | 0.608685 | 0.304343 | − | 0.952563i | \(-0.401563\pi\) | ||||
0.304343 | + | 0.952563i | \(0.401563\pi\) | |||||||
\(140\) | −1.35690 | −0.114679 | ||||||||
\(141\) | 4.82371 | 0.406229 | ||||||||
\(142\) | 11.7506 | 0.986091 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.13706 | 0.426610 | ||||||||
\(146\) | −12.1032 | −1.00167 | ||||||||
\(147\) | 5.15883 | 0.425493 | ||||||||
\(148\) | 2.24698 | 0.184701 | ||||||||
\(149\) | 9.66248 | 0.791581 | 0.395791 | − | 0.918341i | \(-0.370471\pi\) | ||||
0.395791 | + | 0.918341i | \(0.370471\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −7.35152 | −0.598258 | −0.299129 | − | 0.954213i | \(-0.596696\pi\) | ||||
−0.299129 | + | 0.954213i | \(0.596696\pi\) | |||||||
\(152\) | 3.24698 | 0.263365 | ||||||||
\(153\) | −2.04892 | −0.165645 | ||||||||
\(154\) | −7.18598 | −0.579063 | ||||||||
\(155\) | 2.80194 | 0.225057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.85325 | 0.227714 | 0.113857 | − | 0.993497i | \(-0.463679\pi\) | ||||
0.113857 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(158\) | −0.259061 | −0.0206098 | ||||||||
\(159\) | −14.2349 | −1.12890 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.81163 | 0.142776 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −15.1075 | −1.18331 | −0.591656 | − | 0.806190i | \(-0.701526\pi\) | ||||
−0.591656 | + | 0.806190i | \(0.701526\pi\) | |||||||
\(164\) | −10.6310 | −0.830143 | ||||||||
\(165\) | 5.29590 | 0.412285 | ||||||||
\(166\) | 3.02177 | 0.234535 | ||||||||
\(167\) | −16.0881 | −1.24494 | −0.622469 | − | 0.782644i | \(-0.713870\pi\) | ||||
−0.622469 | + | 0.782644i | \(0.713870\pi\) | |||||||
\(168\) | 1.35690 | 0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.04892 | −0.157145 | ||||||||
\(171\) | −3.24698 | −0.248303 | ||||||||
\(172\) | 4.41789 | 0.336861 | ||||||||
\(173\) | −15.4795 | −1.17688 | −0.588442 | − | 0.808540i | \(-0.700258\pi\) | ||||
−0.588442 | + | 0.808540i | \(0.700258\pi\) | |||||||
\(174\) | −5.13706 | −0.389440 | ||||||||
\(175\) | 1.35690 | 0.102572 | ||||||||
\(176\) | 5.29590 | 0.399193 | ||||||||
\(177\) | 13.8998 | 1.04477 | ||||||||
\(178\) | −5.47650 | −0.410481 | ||||||||
\(179\) | 19.0737 | 1.42563 | 0.712817 | − | 0.701351i | \(-0.247419\pi\) | ||||
0.712817 | + | 0.701351i | \(0.247419\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 2.16852 | 0.161185 | 0.0805925 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805925 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.62565 | 0.268015 | ||||||||
\(184\) | −1.33513 | −0.0984268 | ||||||||
\(185\) | −2.24698 | −0.165201 | ||||||||
\(186\) | −2.80194 | −0.205448 | ||||||||
\(187\) | −10.8509 | −0.793493 | ||||||||
\(188\) | −4.82371 | −0.351805 | ||||||||
\(189\) | −1.35690 | −0.0986997 | ||||||||
\(190\) | −3.24698 | −0.235561 | ||||||||
\(191\) | −11.7409 | −0.849545 | −0.424772 | − | 0.905300i | \(-0.639646\pi\) | ||||
−0.424772 | + | 0.905300i | \(0.639646\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 24.6722 | 1.77594 | 0.887971 | − | 0.459900i | \(-0.152115\pi\) | ||||
0.887971 | + | 0.459900i | \(0.152115\pi\) | |||||||
\(194\) | −5.85086 | −0.420067 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.15883 | −0.368488 | ||||||||
\(197\) | −26.2010 | −1.86675 | −0.933374 | − | 0.358906i | \(-0.883150\pi\) | ||||
−0.933374 | + | 0.358906i | \(0.883150\pi\) | |||||||
\(198\) | −5.29590 | −0.376363 | ||||||||
\(199\) | 19.6722 | 1.39452 | 0.697262 | − | 0.716817i | \(-0.254402\pi\) | ||||
0.697262 | + | 0.716817i | \(0.254402\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 9.03684 | 0.637409 | ||||||||
\(202\) | 8.39612 | 0.590749 | ||||||||
\(203\) | −6.97046 | −0.489230 | ||||||||
\(204\) | 2.04892 | 0.143453 | ||||||||
\(205\) | 10.6310 | 0.742503 | ||||||||
\(206\) | −13.6353 | −0.950019 | ||||||||
\(207\) | 1.33513 | 0.0927976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.1957 | −1.18945 | ||||||||
\(210\) | −1.35690 | −0.0936347 | ||||||||
\(211\) | −16.2935 | −1.12169 | −0.560846 | − | 0.827920i | \(-0.689524\pi\) | ||||
−0.560846 | + | 0.827920i | \(0.689524\pi\) | |||||||
\(212\) | 14.2349 | 0.977657 | ||||||||
\(213\) | 11.7506 | 0.805140 | ||||||||
\(214\) | −3.92394 | −0.268235 | ||||||||
\(215\) | −4.41789 | −0.301298 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.80194 | −0.258092 | ||||||||
\(218\) | −0.554958 | −0.0375865 | ||||||||
\(219\) | −12.1032 | −0.817859 | ||||||||
\(220\) | −5.29590 | −0.357049 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.24698 | 0.150807 | ||||||||
\(223\) | 2.28083 | 0.152736 | 0.0763679 | − | 0.997080i | \(-0.475668\pi\) | ||||
0.0763679 | + | 0.997080i | \(0.475668\pi\) | |||||||
\(224\) | −1.35690 | −0.0906614 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −4.39373 | −0.292267 | ||||||||
\(227\) | 3.37196 | 0.223805 | 0.111902 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111902 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(228\) | 3.24698 | 0.215036 | ||||||||
\(229\) | −18.3763 | −1.21434 | −0.607169 | − | 0.794573i | \(-0.707695\pi\) | ||||
−0.607169 | + | 0.794573i | \(0.707695\pi\) | |||||||
\(230\) | 1.33513 | 0.0880356 | ||||||||
\(231\) | −7.18598 | −0.472803 | ||||||||
\(232\) | 5.13706 | 0.337265 | ||||||||
\(233\) | 10.0858 | 0.660740 | 0.330370 | − | 0.943852i | \(-0.392827\pi\) | ||||
0.330370 | + | 0.943852i | \(0.392827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82371 | 0.314664 | ||||||||
\(236\) | −13.8998 | −0.904798 | ||||||||
\(237\) | −0.259061 | −0.0168278 | ||||||||
\(238\) | 2.78017 | 0.180211 | ||||||||
\(239\) | 20.0834 | 1.29908 | 0.649542 | − | 0.760325i | \(-0.274961\pi\) | ||||
0.649542 | + | 0.760325i | \(0.274961\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −2.99462 | −0.192901 | −0.0964503 | − | 0.995338i | \(-0.530749\pi\) | ||||
−0.0964503 | + | 0.995338i | \(0.530749\pi\) | |||||||
\(242\) | −17.0465 | −1.09579 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.62565 | −0.232108 | ||||||||
\(245\) | 5.15883 | 0.329586 | ||||||||
\(246\) | −10.6310 | −0.677809 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.80194 | 0.177923 | ||||||||
\(249\) | 3.02177 | 0.191497 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −7.20237 | −0.454610 | −0.227305 | − | 0.973824i | \(-0.572991\pi\) | ||||
−0.227305 | + | 0.973824i | \(0.572991\pi\) | |||||||
\(252\) | 1.35690 | 0.0854764 | ||||||||
\(253\) | 7.07069 | 0.444530 | ||||||||
\(254\) | 2.23490 | 0.140230 | ||||||||
\(255\) | −2.04892 | −0.128308 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.8291 | −1.17453 | −0.587263 | − | 0.809396i | \(-0.699795\pi\) | ||||
−0.587263 | + | 0.809396i | \(0.699795\pi\) | |||||||
\(258\) | 4.41789 | 0.275046 | ||||||||
\(259\) | 3.04892 | 0.189451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.13706 | −0.317976 | ||||||||
\(262\) | 8.51573 | 0.526104 | ||||||||
\(263\) | −17.9245 | −1.10527 | −0.552637 | − | 0.833422i | \(-0.686378\pi\) | ||||
−0.552637 | + | 0.833422i | \(0.686378\pi\) | |||||||
\(264\) | 5.29590 | 0.325940 | ||||||||
\(265\) | −14.2349 | −0.874443 | ||||||||
\(266\) | 4.40581 | 0.270138 | ||||||||
\(267\) | −5.47650 | −0.335156 | ||||||||
\(268\) | −9.03684 | −0.552013 | ||||||||
\(269\) | −22.4045 | −1.36603 | −0.683013 | − | 0.730406i | \(-0.739331\pi\) | ||||
−0.683013 | + | 0.730406i | \(0.739331\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 23.2325 | 1.41127 | 0.705637 | − | 0.708573i | \(-0.250661\pi\) | ||||
0.705637 | + | 0.708573i | \(0.250661\pi\) | |||||||
\(272\) | −2.04892 | −0.124234 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.1685 | 0.795540 | ||||||||
\(275\) | 5.29590 | 0.319355 | ||||||||
\(276\) | −1.33513 | −0.0803651 | ||||||||
\(277\) | −9.78448 | −0.587892 | −0.293946 | − | 0.955822i | \(-0.594969\pi\) | ||||
−0.293946 | + | 0.955822i | \(0.594969\pi\) | |||||||
\(278\) | −7.17629 | −0.430405 | ||||||||
\(279\) | −2.80194 | −0.167748 | ||||||||
\(280\) | 1.35690 | 0.0810900 | ||||||||
\(281\) | −21.6286 | −1.29026 | −0.645128 | − | 0.764075i | \(-0.723196\pi\) | ||||
−0.645128 | + | 0.764075i | \(0.723196\pi\) | |||||||
\(282\) | −4.82371 | −0.287248 | ||||||||
\(283\) | 3.38942 | 0.201480 | 0.100740 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100740 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(284\) | −11.7506 | −0.697271 | ||||||||
\(285\) | −3.24698 | −0.192334 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.4252 | −0.851492 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −12.8019 | −0.753055 | ||||||||
\(290\) | −5.13706 | −0.301659 | ||||||||
\(291\) | −5.85086 | −0.342983 | ||||||||
\(292\) | 12.1032 | 0.708287 | ||||||||
\(293\) | −34.1280 | −1.99378 | −0.996889 | − | 0.0788243i | \(-0.974883\pi\) | ||||
−0.996889 | + | 0.0788243i | \(0.974883\pi\) | |||||||
\(294\) | −5.15883 | −0.300869 | ||||||||
\(295\) | 13.8998 | 0.809276 | ||||||||
\(296\) | −2.24698 | −0.130603 | ||||||||
\(297\) | −5.29590 | −0.307299 | ||||||||
\(298\) | −9.66248 | −0.559733 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 5.99462 | 0.345524 | ||||||||
\(302\) | 7.35152 | 0.423032 | ||||||||
\(303\) | 8.39612 | 0.482345 | ||||||||
\(304\) | −3.24698 | −0.186227 | ||||||||
\(305\) | 3.62565 | 0.207604 | ||||||||
\(306\) | 2.04892 | 0.117129 | ||||||||
\(307\) | 15.6601 | 0.893768 | 0.446884 | − | 0.894592i | \(-0.352534\pi\) | ||||
0.446884 | + | 0.894592i | \(0.352534\pi\) | |||||||
\(308\) | 7.18598 | 0.409459 | ||||||||
\(309\) | −13.6353 | −0.775687 | ||||||||
\(310\) | −2.80194 | −0.159139 | ||||||||
\(311\) | 25.7972 | 1.46282 | 0.731411 | − | 0.681937i | \(-0.238862\pi\) | ||||
0.731411 | + | 0.681937i | \(0.238862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6243 | −0.883139 | −0.441569 | − | 0.897227i | \(-0.645578\pi\) | ||||
−0.441569 | + | 0.897227i | \(0.645578\pi\) | |||||||
\(314\) | −2.85325 | −0.161018 | ||||||||
\(315\) | −1.35690 | −0.0764524 | ||||||||
\(316\) | 0.259061 | 0.0145733 | ||||||||
\(317\) | 9.25965 | 0.520074 | 0.260037 | − | 0.965599i | \(-0.416265\pi\) | ||||
0.260037 | + | 0.965599i | \(0.416265\pi\) | |||||||
\(318\) | 14.2349 | 0.798253 | ||||||||
\(319\) | −27.2054 | −1.52321 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.92394 | −0.219013 | ||||||||
\(322\) | −1.81163 | −0.100958 | ||||||||
\(323\) | 6.65279 | 0.370171 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.1075 | 0.836728 | ||||||||
\(327\) | −0.554958 | −0.0306893 | ||||||||
\(328\) | 10.6310 | 0.587000 | ||||||||
\(329\) | −6.54527 | −0.360852 | ||||||||
\(330\) | −5.29590 | −0.291530 | ||||||||
\(331\) | −21.8582 | −1.20143 | −0.600716 | − | 0.799462i | \(-0.705118\pi\) | ||||
−0.600716 | + | 0.799462i | \(0.705118\pi\) | |||||||
\(332\) | −3.02177 | −0.165841 | ||||||||
\(333\) | 2.24698 | 0.123134 | ||||||||
\(334\) | 16.0881 | 0.880304 | ||||||||
\(335\) | 9.03684 | 0.493735 | ||||||||
\(336\) | −1.35690 | −0.0740247 | ||||||||
\(337\) | 14.5013 | 0.789934 | 0.394967 | − | 0.918695i | \(-0.370756\pi\) | ||||
0.394967 | + | 0.918695i | \(0.370756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.39373 | −0.238635 | ||||||||
\(340\) | 2.04892 | 0.111118 | ||||||||
\(341\) | −14.8388 | −0.803565 | ||||||||
\(342\) | 3.24698 | 0.175577 | ||||||||
\(343\) | −16.4983 | −0.890823 | ||||||||
\(344\) | −4.41789 | −0.238197 | ||||||||
\(345\) | 1.33513 | 0.0718807 | ||||||||
\(346\) | 15.4795 | 0.832182 | ||||||||
\(347\) | 7.84117 | 0.420936 | 0.210468 | − | 0.977601i | \(-0.432501\pi\) | ||||
0.210468 | + | 0.977601i | \(0.432501\pi\) | |||||||
\(348\) | 5.13706 | 0.275375 | ||||||||
\(349\) | −20.4252 | −1.09334 | −0.546668 | − | 0.837350i | \(-0.684104\pi\) | ||||
−0.546668 | + | 0.837350i | \(0.684104\pi\) | |||||||
\(350\) | −1.35690 | −0.0725291 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.29590 | −0.282272 | ||||||||
\(353\) | −13.2905 | −0.707383 | −0.353692 | − | 0.935362i | \(-0.615074\pi\) | ||||
−0.353692 | + | 0.935362i | \(0.615074\pi\) | |||||||
\(354\) | −13.8998 | −0.738765 | ||||||||
\(355\) | 11.7506 | 0.623659 | ||||||||
\(356\) | 5.47650 | 0.290254 | ||||||||
\(357\) | 2.78017 | 0.147142 | ||||||||
\(358\) | −19.0737 | −1.00807 | ||||||||
\(359\) | 12.8267 | 0.676967 | 0.338483 | − | 0.940972i | \(-0.390086\pi\) | ||||
0.338483 | + | 0.940972i | \(0.390086\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −8.45712 | −0.445112 | ||||||||
\(362\) | −2.16852 | −0.113975 | ||||||||
\(363\) | −17.0465 | −0.894710 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1032 | −0.633511 | ||||||||
\(366\) | −3.62565 | −0.189516 | ||||||||
\(367\) | −17.9554 | −0.937264 | −0.468632 | − | 0.883393i | \(-0.655253\pi\) | ||||
−0.468632 | + | 0.883393i | \(0.655253\pi\) | |||||||
\(368\) | 1.33513 | 0.0695982 | ||||||||
\(369\) | −10.6310 | −0.553429 | ||||||||
\(370\) | 2.24698 | 0.116815 | ||||||||
\(371\) | 19.3153 | 1.00280 | ||||||||
\(372\) | 2.80194 | 0.145274 | ||||||||
\(373\) | 27.8732 | 1.44322 | 0.721610 | − | 0.692300i | \(-0.243402\pi\) | ||||
0.721610 | + | 0.692300i | \(0.243402\pi\) | |||||||
\(374\) | 10.8509 | 0.561084 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 4.82371 | 0.248764 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.35690 | 0.0697912 | ||||||||
\(379\) | 13.8702 | 0.712466 | 0.356233 | − | 0.934397i | \(-0.384061\pi\) | ||||
0.356233 | + | 0.934397i | \(0.384061\pi\) | |||||||
\(380\) | 3.24698 | 0.166567 | ||||||||
\(381\) | 2.23490 | 0.114497 | ||||||||
\(382\) | 11.7409 | 0.600719 | ||||||||
\(383\) | −26.8984 | −1.37445 | −0.687223 | − | 0.726446i | \(-0.741171\pi\) | ||||
−0.687223 | + | 0.726446i | \(0.741171\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −7.18598 | −0.366231 | ||||||||
\(386\) | −24.6722 | −1.25578 | ||||||||
\(387\) | 4.41789 | 0.224574 | ||||||||
\(388\) | 5.85086 | 0.297032 | ||||||||
\(389\) | −0.187309 | −0.00949693 | −0.00474846 | − | 0.999989i | \(-0.501511\pi\) | ||||
−0.00474846 | + | 0.999989i | \(0.501511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.73556 | −0.138343 | ||||||||
\(392\) | 5.15883 | 0.260560 | ||||||||
\(393\) | 8.51573 | 0.429562 | ||||||||
\(394\) | 26.2010 | 1.31999 | ||||||||
\(395\) | −0.259061 | −0.0130348 | ||||||||
\(396\) | 5.29590 | 0.266129 | ||||||||
\(397\) | −8.58211 | −0.430724 | −0.215362 | − | 0.976534i | \(-0.569093\pi\) | ||||
−0.215362 | + | 0.976534i | \(0.569093\pi\) | |||||||
\(398\) | −19.6722 | −0.986077 | ||||||||
\(399\) | 4.40581 | 0.220567 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −23.9748 | −1.19724 | −0.598621 | − | 0.801032i | \(-0.704285\pi\) | ||||
−0.598621 | + | 0.801032i | \(0.704285\pi\) | |||||||
\(402\) | −9.03684 | −0.450716 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.39612 | −0.417723 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 6.97046 | 0.345938 | ||||||||
\(407\) | 11.8998 | 0.589850 | ||||||||
\(408\) | −2.04892 | −0.101437 | ||||||||
\(409\) | 8.37926 | 0.414328 | 0.207164 | − | 0.978306i | \(-0.433577\pi\) | ||||
0.207164 | + | 0.978306i | \(0.433577\pi\) | |||||||
\(410\) | −10.6310 | −0.525029 | ||||||||
\(411\) | 13.1685 | 0.649555 | ||||||||
\(412\) | 13.6353 | 0.671765 | ||||||||
\(413\) | −18.8605 | −0.928067 | ||||||||
\(414\) | −1.33513 | −0.0656178 | ||||||||
\(415\) | 3.02177 | 0.148333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.17629 | −0.351425 | ||||||||
\(418\) | 17.1957 | 0.841068 | ||||||||
\(419\) | 37.0887 | 1.81190 | 0.905952 | − | 0.423381i | \(-0.139157\pi\) | ||||
0.905952 | + | 0.423381i | \(0.139157\pi\) | |||||||
\(420\) | 1.35690 | 0.0662097 | ||||||||
\(421\) | −4.90515 | −0.239062 | −0.119531 | − | 0.992830i | \(-0.538139\pi\) | ||||
−0.119531 | + | 0.992830i | \(0.538139\pi\) | |||||||
\(422\) | 16.2935 | 0.793155 | ||||||||
\(423\) | −4.82371 | −0.234537 | ||||||||
\(424\) | −14.2349 | −0.691308 | ||||||||
\(425\) | −2.04892 | −0.0993871 | ||||||||
\(426\) | −11.7506 | −0.569320 | ||||||||
\(427\) | −4.91962 | −0.238077 | ||||||||
\(428\) | 3.92394 | 0.189671 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.41789 | 0.213050 | ||||||||
\(431\) | 6.06531 | 0.292156 | 0.146078 | − | 0.989273i | \(-0.453335\pi\) | ||||
0.146078 | + | 0.989273i | \(0.453335\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −14.8877 | −0.715457 | −0.357728 | − | 0.933826i | \(-0.616449\pi\) | ||||
−0.357728 | + | 0.933826i | \(0.616449\pi\) | |||||||
\(434\) | 3.80194 | 0.182499 | ||||||||
\(435\) | −5.13706 | −0.246303 | ||||||||
\(436\) | 0.554958 | 0.0265777 | ||||||||
\(437\) | −4.33513 | −0.207377 | ||||||||
\(438\) | 12.1032 | 0.578314 | ||||||||
\(439\) | −21.1336 | −1.00865 | −0.504326 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504326 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(440\) | 5.29590 | 0.252472 | ||||||||
\(441\) | −5.15883 | −0.245659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0683 | 1.33356 | 0.666782 | − | 0.745252i | \(-0.267671\pi\) | ||||
0.666782 | + | 0.745252i | \(0.267671\pi\) | |||||||
\(444\) | −2.24698 | −0.106637 | ||||||||
\(445\) | −5.47650 | −0.259611 | ||||||||
\(446\) | −2.28083 | −0.108000 | ||||||||
\(447\) | −9.66248 | −0.457020 | ||||||||
\(448\) | 1.35690 | 0.0641073 | ||||||||
\(449\) | −19.2446 | −0.908208 | −0.454104 | − | 0.890949i | \(-0.650041\pi\) | ||||
−0.454104 | + | 0.890949i | \(0.650041\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −56.3008 | −2.65110 | ||||||||
\(452\) | 4.39373 | 0.206664 | ||||||||
\(453\) | 7.35152 | 0.345404 | ||||||||
\(454\) | −3.37196 | −0.158254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.24698 | −0.152054 | ||||||||
\(457\) | 37.8485 | 1.77048 | 0.885238 | − | 0.465138i | \(-0.153995\pi\) | ||||
0.885238 | + | 0.465138i | \(0.153995\pi\) | |||||||
\(458\) | 18.3763 | 0.858667 | ||||||||
\(459\) | 2.04892 | 0.0956353 | ||||||||
\(460\) | −1.33513 | −0.0622506 | ||||||||
\(461\) | 11.2228 | 0.522699 | 0.261349 | − | 0.965244i | \(-0.415833\pi\) | ||||
0.261349 | + | 0.965244i | \(0.415833\pi\) | |||||||
\(462\) | 7.18598 | 0.334322 | ||||||||
\(463\) | −25.0726 | −1.16522 | −0.582611 | − | 0.812751i | \(-0.697969\pi\) | ||||
−0.582611 | + | 0.812751i | \(0.697969\pi\) | |||||||
\(464\) | −5.13706 | −0.238482 | ||||||||
\(465\) | −2.80194 | −0.129937 | ||||||||
\(466\) | −10.0858 | −0.467213 | ||||||||
\(467\) | 36.9657 | 1.71057 | 0.855284 | − | 0.518160i | \(-0.173383\pi\) | ||||
0.855284 | + | 0.518160i | \(0.173383\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2620 | −0.566209 | ||||||||
\(470\) | −4.82371 | −0.222501 | ||||||||
\(471\) | −2.85325 | −0.131471 | ||||||||
\(472\) | 13.8998 | 0.639789 | ||||||||
\(473\) | 23.3967 | 1.07578 | ||||||||
\(474\) | 0.259061 | 0.0118991 | ||||||||
\(475\) | −3.24698 | −0.148982 | ||||||||
\(476\) | −2.78017 | −0.127429 | ||||||||
\(477\) | 14.2349 | 0.651771 | ||||||||
\(478\) | −20.0834 | −0.918592 | ||||||||
\(479\) | −31.4590 | −1.43740 | −0.718700 | − | 0.695320i | \(-0.755263\pi\) | ||||
−0.718700 | + | 0.695320i | \(0.755263\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.99462 | 0.136401 | ||||||||
\(483\) | −1.81163 | −0.0824319 | ||||||||
\(484\) | 17.0465 | 0.774842 | ||||||||
\(485\) | −5.85086 | −0.265674 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −18.8713 | −0.855140 | −0.427570 | − | 0.903982i | \(-0.640630\pi\) | ||||
−0.427570 | + | 0.903982i | \(0.640630\pi\) | |||||||
\(488\) | 3.62565 | 0.164125 | ||||||||
\(489\) | 15.1075 | 0.683186 | ||||||||
\(490\) | −5.15883 | −0.233052 | ||||||||
\(491\) | −16.3961 | −0.739947 | −0.369973 | − | 0.929042i | \(-0.620633\pi\) | ||||
−0.369973 | + | 0.929042i | \(0.620633\pi\) | |||||||
\(492\) | 10.6310 | 0.479284 | ||||||||
\(493\) | 10.5254 | 0.474041 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.29590 | −0.238033 | ||||||||
\(496\) | −2.80194 | −0.125811 | ||||||||
\(497\) | −15.9444 | −0.715203 | ||||||||
\(498\) | −3.02177 | −0.135409 | ||||||||
\(499\) | −40.2452 | −1.80162 | −0.900811 | − | 0.434212i | \(-0.857027\pi\) | ||||
−0.900811 | + | 0.434212i | \(0.857027\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 16.0881 | 0.718765 | ||||||||
\(502\) | 7.20237 | 0.321458 | ||||||||
\(503\) | 18.4004 | 0.820435 | 0.410217 | − | 0.911988i | \(-0.365453\pi\) | ||||
0.410217 | + | 0.911988i | \(0.365453\pi\) | |||||||
\(504\) | −1.35690 | −0.0604409 | ||||||||
\(505\) | 8.39612 | 0.373623 | ||||||||
\(506\) | −7.07069 | −0.314330 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.23490 | −0.0991576 | ||||||||
\(509\) | 35.1377 | 1.55745 | 0.778725 | − | 0.627366i | \(-0.215867\pi\) | ||||
0.778725 | + | 0.627366i | \(0.215867\pi\) | |||||||
\(510\) | 2.04892 | 0.0907276 | ||||||||
\(511\) | 16.4228 | 0.726502 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.24698 | 0.143358 | ||||||||
\(514\) | 18.8291 | 0.830515 | ||||||||
\(515\) | −13.6353 | −0.600845 | ||||||||
\(516\) | −4.41789 | −0.194487 | ||||||||
\(517\) | −25.5459 | −1.12351 | ||||||||
\(518\) | −3.04892 | −0.133962 | ||||||||
\(519\) | 15.4795 | 0.679474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2610 | −1.54481 | −0.772406 | − | 0.635129i | \(-0.780947\pi\) | ||||
−0.772406 | + | 0.635129i | \(0.780947\pi\) | |||||||
\(522\) | 5.13706 | 0.224843 | ||||||||
\(523\) | 14.3043 | 0.625482 | 0.312741 | − | 0.949839i | \(-0.398753\pi\) | ||||
0.312741 | + | 0.949839i | \(0.398753\pi\) | |||||||
\(524\) | −8.51573 | −0.372011 | ||||||||
\(525\) | −1.35690 | −0.0592198 | ||||||||
\(526\) | 17.9245 | 0.781546 | ||||||||
\(527\) | 5.74094 | 0.250079 | ||||||||
\(528\) | −5.29590 | −0.230474 | ||||||||
\(529\) | −21.2174 | −0.922497 | ||||||||
\(530\) | 14.2349 | 0.618324 | ||||||||
\(531\) | −13.8998 | −0.603199 | ||||||||
\(532\) | −4.40581 | −0.191016 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.47650 | 0.236991 | ||||||||
\(535\) | −3.92394 | −0.169647 | ||||||||
\(536\) | 9.03684 | 0.390332 | ||||||||
\(537\) | −19.0737 | −0.823090 | ||||||||
\(538\) | 22.4045 | 0.965926 | ||||||||
\(539\) | −27.3207 | −1.17678 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 44.2422 | 1.90212 | 0.951060 | − | 0.309006i | \(-0.0999962\pi\) | ||||
0.951060 | + | 0.309006i | \(0.0999962\pi\) | |||||||
\(542\) | −23.2325 | −0.997922 | ||||||||
\(543\) | −2.16852 | −0.0930602 | ||||||||
\(544\) | 2.04892 | 0.0878466 | ||||||||
\(545\) | −0.554958 | −0.0237718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.34481 | 0.271285 | 0.135642 | − | 0.990758i | \(-0.456690\pi\) | ||||
0.135642 | + | 0.990758i | \(0.456690\pi\) | |||||||
\(548\) | −13.1685 | −0.562531 | ||||||||
\(549\) | −3.62565 | −0.154739 | ||||||||
\(550\) | −5.29590 | −0.225818 | ||||||||
\(551\) | 16.6799 | 0.710589 | ||||||||
\(552\) | 1.33513 | 0.0568267 | ||||||||
\(553\) | 0.351519 | 0.0149481 | ||||||||
\(554\) | 9.78448 | 0.415703 | ||||||||
\(555\) | 2.24698 | 0.0953790 | ||||||||
\(556\) | 7.17629 | 0.304343 | ||||||||
\(557\) | −31.3884 | −1.32997 | −0.664984 | − | 0.746858i | \(-0.731562\pi\) | ||||
−0.664984 | + | 0.746858i | \(0.731562\pi\) | |||||||
\(558\) | 2.80194 | 0.118615 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.35690 | −0.0573393 | ||||||||
\(561\) | 10.8509 | 0.458123 | ||||||||
\(562\) | 21.6286 | 0.912349 | ||||||||
\(563\) | −44.4989 | −1.87540 | −0.937702 | − | 0.347441i | \(-0.887051\pi\) | ||||
−0.937702 | + | 0.347441i | \(0.887051\pi\) | |||||||
\(564\) | 4.82371 | 0.203115 | ||||||||
\(565\) | −4.39373 | −0.184846 | ||||||||
\(566\) | −3.38942 | −0.142468 | ||||||||
\(567\) | 1.35690 | 0.0569843 | ||||||||
\(568\) | 11.7506 | 0.493045 | ||||||||
\(569\) | 30.5394 | 1.28028 | 0.640140 | − | 0.768259i | \(-0.278877\pi\) | ||||
0.640140 | + | 0.768259i | \(0.278877\pi\) | |||||||
\(570\) | 3.24698 | 0.136001 | ||||||||
\(571\) | −32.7614 | −1.37102 | −0.685511 | − | 0.728063i | \(-0.740421\pi\) | ||||
−0.685511 | + | 0.728063i | \(0.740421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.7409 | 0.490485 | ||||||||
\(574\) | 14.4252 | 0.602096 | ||||||||
\(575\) | 1.33513 | 0.0556786 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −36.5870 | −1.52314 | −0.761569 | − | 0.648084i | \(-0.775570\pi\) | ||||
−0.761569 | + | 0.648084i | \(0.775570\pi\) | |||||||
\(578\) | 12.8019 | 0.532490 | ||||||||
\(579\) | −24.6722 | −1.02534 | ||||||||
\(580\) | 5.13706 | 0.213305 | ||||||||
\(581\) | −4.10023 | −0.170106 | ||||||||
\(582\) | 5.85086 | 0.242526 | ||||||||
\(583\) | 75.3866 | 3.12219 | ||||||||
\(584\) | −12.1032 | −0.500834 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.1280 | 1.40981 | ||||||||
\(587\) | −22.4873 | −0.928148 | −0.464074 | − | 0.885796i | \(-0.653613\pi\) | ||||
−0.464074 | + | 0.885796i | \(0.653613\pi\) | |||||||
\(588\) | 5.15883 | 0.212747 | ||||||||
\(589\) | 9.09783 | 0.374870 | ||||||||
\(590\) | −13.8998 | −0.572245 | ||||||||
\(591\) | 26.2010 | 1.07777 | ||||||||
\(592\) | 2.24698 | 0.0923503 | ||||||||
\(593\) | −39.5749 | −1.62515 | −0.812574 | − | 0.582858i | \(-0.801934\pi\) | ||||
−0.812574 | + | 0.582858i | \(0.801934\pi\) | |||||||
\(594\) | 5.29590 | 0.217293 | ||||||||
\(595\) | 2.78017 | 0.113976 | ||||||||
\(596\) | 9.66248 | 0.395791 | ||||||||
\(597\) | −19.6722 | −0.805128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.3424 | −1.28062 | −0.640308 | − | 0.768118i | \(-0.721193\pi\) | ||||
−0.640308 | + | 0.768118i | \(0.721193\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −32.9487 | −1.34401 | −0.672003 | − | 0.740549i | \(-0.734566\pi\) | ||||
−0.672003 | + | 0.740549i | \(0.734566\pi\) | |||||||
\(602\) | −5.99462 | −0.244323 | ||||||||
\(603\) | −9.03684 | −0.368008 | ||||||||
\(604\) | −7.35152 | −0.299129 | ||||||||
\(605\) | −17.0465 | −0.693040 | ||||||||
\(606\) | −8.39612 | −0.341069 | ||||||||
\(607\) | −40.1739 | −1.63061 | −0.815304 | − | 0.579033i | \(-0.803430\pi\) | ||||
−0.815304 | + | 0.579033i | \(0.803430\pi\) | |||||||
\(608\) | 3.24698 | 0.131682 | ||||||||
\(609\) | 6.97046 | 0.282457 | ||||||||
\(610\) | −3.62565 | −0.146798 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.04892 | −0.0828226 | ||||||||
\(613\) | −11.3588 | −0.458778 | −0.229389 | − | 0.973335i | \(-0.573673\pi\) | ||||
−0.229389 | + | 0.973335i | \(0.573673\pi\) | |||||||
\(614\) | −15.6601 | −0.631990 | ||||||||
\(615\) | −10.6310 | −0.428684 | ||||||||
\(616\) | −7.18598 | −0.289531 | ||||||||
\(617\) | −20.9172 | −0.842096 | −0.421048 | − | 0.907038i | \(-0.638338\pi\) | ||||
−0.421048 | + | 0.907038i | \(0.638338\pi\) | |||||||
\(618\) | 13.6353 | 0.548494 | ||||||||
\(619\) | 14.0562 | 0.564967 | 0.282483 | − | 0.959272i | \(-0.408842\pi\) | ||||
0.282483 | + | 0.959272i | \(0.408842\pi\) | |||||||
\(620\) | 2.80194 | 0.112529 | ||||||||
\(621\) | −1.33513 | −0.0535767 | ||||||||
\(622\) | −25.7972 | −1.03437 | ||||||||
\(623\) | 7.43104 | 0.297718 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 15.6243 | 0.624473 | ||||||||
\(627\) | 17.1957 | 0.686729 | ||||||||
\(628\) | 2.85325 | 0.113857 | ||||||||
\(629\) | −4.60388 | −0.183569 | ||||||||
\(630\) | 1.35690 | 0.0540600 | ||||||||
\(631\) | 40.6601 | 1.61865 | 0.809326 | − | 0.587359i | \(-0.199832\pi\) | ||||
0.809326 | + | 0.587359i | \(0.199832\pi\) | |||||||
\(632\) | −0.259061 | −0.0103049 | ||||||||
\(633\) | 16.2935 | 0.647609 | ||||||||
\(634\) | −9.25965 | −0.367748 | ||||||||
\(635\) | 2.23490 | 0.0886892 | ||||||||
\(636\) | −14.2349 | −0.564450 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 27.2054 | 1.07707 | ||||||||
\(639\) | −11.7506 | −0.464848 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −1.92633 | −0.0760854 | −0.0380427 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380427 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(642\) | 3.92394 | 0.154865 | ||||||||
\(643\) | −3.37973 | −0.133284 | −0.0666418 | − | 0.997777i | \(-0.521228\pi\) | ||||
−0.0666418 | + | 0.997777i | \(0.521228\pi\) | |||||||
\(644\) | 1.81163 | 0.0713881 | ||||||||
\(645\) | 4.41789 | 0.173954 | ||||||||
\(646\) | −6.65279 | −0.261751 | ||||||||
\(647\) | −10.8181 | −0.425302 | −0.212651 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212651 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −73.6118 | −2.88951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.80194 | 0.149010 | ||||||||
\(652\) | −15.1075 | −0.591656 | ||||||||
\(653\) | 33.7646 | 1.32131 | 0.660656 | − | 0.750689i | \(-0.270278\pi\) | ||||
0.660656 | + | 0.750689i | \(0.270278\pi\) | |||||||
\(654\) | 0.554958 | 0.0217006 | ||||||||
\(655\) | 8.51573 | 0.332737 | ||||||||
\(656\) | −10.6310 | −0.415072 | ||||||||
\(657\) | 12.1032 | 0.472191 | ||||||||
\(658\) | 6.54527 | 0.255161 | ||||||||
\(659\) | −16.8592 | −0.656742 | −0.328371 | − | 0.944549i | \(-0.606500\pi\) | ||||
−0.328371 | + | 0.944549i | \(0.606500\pi\) | |||||||
\(660\) | 5.29590 | 0.206143 | ||||||||
\(661\) | 4.71140 | 0.183252 | 0.0916261 | − | 0.995793i | \(-0.470794\pi\) | ||||
0.0916261 | + | 0.995793i | \(0.470794\pi\) | |||||||
\(662\) | 21.8582 | 0.849541 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.02177 | 0.117267 | ||||||||
\(665\) | 4.40581 | 0.170850 | ||||||||
\(666\) | −2.24698 | −0.0870687 | ||||||||
\(667\) | −6.85862 | −0.265567 | ||||||||
\(668\) | −16.0881 | −0.622469 | ||||||||
\(669\) | −2.28083 | −0.0881820 | ||||||||
\(670\) | −9.03684 | −0.349123 | ||||||||
\(671\) | −19.2010 | −0.741248 | ||||||||
\(672\) | 1.35690 | 0.0523434 | ||||||||
\(673\) | 3.12797 | 0.120574 | 0.0602871 | − | 0.998181i | \(-0.480798\pi\) | ||||
0.0602871 | + | 0.998181i | \(0.480798\pi\) | |||||||
\(674\) | −14.5013 | −0.558567 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.50737 | −0.0579329 | −0.0289664 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289664 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(678\) | 4.39373 | 0.168740 | ||||||||
\(679\) | 7.93900 | 0.304671 | ||||||||
\(680\) | −2.04892 | −0.0785724 | ||||||||
\(681\) | −3.37196 | −0.129214 | ||||||||
\(682\) | 14.8388 | 0.568206 | ||||||||
\(683\) | 31.0726 | 1.18896 | 0.594480 | − | 0.804110i | \(-0.297358\pi\) | ||||
0.594480 | + | 0.804110i | \(0.297358\pi\) | |||||||
\(684\) | −3.24698 | −0.124151 | ||||||||
\(685\) | 13.1685 | 0.503143 | ||||||||
\(686\) | 16.4983 | 0.629907 | ||||||||
\(687\) | 18.3763 | 0.701099 | ||||||||
\(688\) | 4.41789 | 0.168431 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.33513 | −0.0508274 | ||||||||
\(691\) | −26.7469 | −1.01750 | −0.508750 | − | 0.860914i | \(-0.669892\pi\) | ||||
−0.508750 | + | 0.860914i | \(0.669892\pi\) | |||||||
\(692\) | −15.4795 | −0.588442 | ||||||||
\(693\) | 7.18598 | 0.272973 | ||||||||
\(694\) | −7.84117 | −0.297647 | ||||||||
\(695\) | −7.17629 | −0.272212 | ||||||||
\(696\) | −5.13706 | −0.194720 | ||||||||
\(697\) | 21.7821 | 0.825055 | ||||||||
\(698\) | 20.4252 | 0.773105 | ||||||||
\(699\) | −10.0858 | −0.381478 | ||||||||
\(700\) | 1.35690 | 0.0512858 | ||||||||
\(701\) | 11.2054 | 0.423221 | 0.211610 | − | 0.977354i | \(-0.432129\pi\) | ||||
0.211610 | + | 0.977354i | \(0.432129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.29590 | −0.275170 | ||||||||
\(704\) | 5.29590 | 0.199597 | ||||||||
\(705\) | −4.82371 | −0.181671 | ||||||||
\(706\) | 13.2905 | 0.500195 | ||||||||
\(707\) | −11.3927 | −0.428465 | ||||||||
\(708\) | 13.8998 | 0.522385 | ||||||||
\(709\) | 26.9933 | 1.01375 | 0.506877 | − | 0.862018i | \(-0.330800\pi\) | ||||
0.506877 | + | 0.862018i | \(0.330800\pi\) | |||||||
\(710\) | −11.7506 | −0.440993 | ||||||||
\(711\) | 0.259061 | 0.00971555 | ||||||||
\(712\) | −5.47650 | −0.205241 | ||||||||
\(713\) | −3.74094 | −0.140099 | ||||||||
\(714\) | −2.78017 | −0.104045 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.0737 | 0.712817 | ||||||||
\(717\) | −20.0834 | −0.750027 | ||||||||
\(718\) | −12.8267 | −0.478688 | ||||||||
\(719\) | −15.4601 | −0.576565 | −0.288282 | − | 0.957545i | \(-0.593084\pi\) | ||||
−0.288282 | + | 0.957545i | \(0.593084\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 18.5017 | 0.689040 | ||||||||
\(722\) | 8.45712 | 0.314742 | ||||||||
\(723\) | 2.99462 | 0.111371 | ||||||||
\(724\) | 2.16852 | 0.0805925 | ||||||||
\(725\) | −5.13706 | −0.190786 | ||||||||
\(726\) | 17.0465 | 0.632656 | ||||||||
\(727\) | −10.9148 | −0.404809 | −0.202404 | − | 0.979302i | \(-0.564876\pi\) | ||||
−0.202404 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.1032 | 0.447960 | ||||||||
\(731\) | −9.05190 | −0.334797 | ||||||||
\(732\) | 3.62565 | 0.134008 | ||||||||
\(733\) | −13.5539 | −0.500624 | −0.250312 | − | 0.968165i | \(-0.580533\pi\) | ||||
−0.250312 | + | 0.968165i | \(0.580533\pi\) | |||||||
\(734\) | 17.9554 | 0.662746 | ||||||||
\(735\) | −5.15883 | −0.190286 | ||||||||
\(736\) | −1.33513 | −0.0492134 | ||||||||
\(737\) | −47.8582 | −1.76288 | ||||||||
\(738\) | 10.6310 | 0.391333 | ||||||||
\(739\) | 15.4679 | 0.568995 | 0.284498 | − | 0.958677i | \(-0.408173\pi\) | ||||
0.284498 | + | 0.958677i | \(0.408173\pi\) | |||||||
\(740\) | −2.24698 | −0.0826006 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.3153 | −0.709086 | ||||||||
\(743\) | 40.2040 | 1.47494 | 0.737471 | − | 0.675378i | \(-0.236020\pi\) | ||||
0.737471 | + | 0.675378i | \(0.236020\pi\) | |||||||
\(744\) | −2.80194 | −0.102724 | ||||||||
\(745\) | −9.66248 | −0.354006 | ||||||||
\(746\) | −27.8732 | −1.02051 | ||||||||
\(747\) | −3.02177 | −0.110561 | ||||||||
\(748\) | −10.8509 | −0.396747 | ||||||||
\(749\) | 5.32437 | 0.194548 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −19.8465 | −0.724211 | −0.362105 | − | 0.932137i | \(-0.617942\pi\) | ||||
−0.362105 | + | 0.932137i | \(0.617942\pi\) | |||||||
\(752\) | −4.82371 | −0.175903 | ||||||||
\(753\) | 7.20237 | 0.262469 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.35152 | 0.267549 | ||||||||
\(756\) | −1.35690 | −0.0493498 | ||||||||
\(757\) | 39.8883 | 1.44976 | 0.724882 | − | 0.688873i | \(-0.241894\pi\) | ||||
0.724882 | + | 0.688873i | \(0.241894\pi\) | |||||||
\(758\) | −13.8702 | −0.503790 | ||||||||
\(759\) | −7.07069 | −0.256650 | ||||||||
\(760\) | −3.24698 | −0.117780 | ||||||||
\(761\) | 31.8756 | 1.15549 | 0.577745 | − | 0.816217i | \(-0.303933\pi\) | ||||
0.577745 | + | 0.816217i | \(0.303933\pi\) | |||||||
\(762\) | −2.23490 | −0.0809618 | ||||||||
\(763\) | 0.753020 | 0.0272612 | ||||||||
\(764\) | −11.7409 | −0.424772 | ||||||||
\(765\) | 2.04892 | 0.0740788 | ||||||||
\(766\) | 26.8984 | 0.971880 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −43.0672 | −1.55304 | −0.776522 | − | 0.630090i | \(-0.783018\pi\) | ||||
−0.776522 | + | 0.630090i | \(0.783018\pi\) | |||||||
\(770\) | 7.18598 | 0.258965 | ||||||||
\(771\) | 18.8291 | 0.678113 | ||||||||
\(772\) | 24.6722 | 0.887971 | ||||||||
\(773\) | 33.1282 | 1.19154 | 0.595770 | − | 0.803155i | \(-0.296847\pi\) | ||||
0.595770 | + | 0.803155i | \(0.296847\pi\) | |||||||
\(774\) | −4.41789 | −0.158798 | ||||||||
\(775\) | −2.80194 | −0.100649 | ||||||||
\(776\) | −5.85086 | −0.210033 | ||||||||
\(777\) | −3.04892 | −0.109379 | ||||||||
\(778\) | 0.187309 | 0.00671534 | ||||||||
\(779\) | 34.5187 | 1.23676 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.2301 | −2.22677 | ||||||||
\(782\) | 2.73556 | 0.0978235 | ||||||||
\(783\) | 5.13706 | 0.183584 | ||||||||
\(784\) | −5.15883 | −0.184244 | ||||||||
\(785\) | −2.85325 | −0.101837 | ||||||||
\(786\) | −8.51573 | −0.303746 | ||||||||
\(787\) | 35.9138 | 1.28019 | 0.640094 | − | 0.768297i | \(-0.278895\pi\) | ||||
0.640094 | + | 0.768297i | \(0.278895\pi\) | |||||||
\(788\) | −26.2010 | −0.933374 | ||||||||
\(789\) | 17.9245 | 0.638130 | ||||||||
\(790\) | 0.259061 | 0.00921698 | ||||||||
\(791\) | 5.96184 | 0.211978 | ||||||||
\(792\) | −5.29590 | −0.188182 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.58211 | 0.304568 | ||||||||
\(795\) | 14.2349 | 0.504860 | ||||||||
\(796\) | 19.6722 | 0.697262 | ||||||||
\(797\) | −29.7918 | −1.05528 | −0.527639 | − | 0.849468i | \(-0.676923\pi\) | ||||
−0.527639 | + | 0.849468i | \(0.676923\pi\) | |||||||
\(798\) | −4.40581 | −0.155964 | ||||||||
\(799\) | 9.88338 | 0.349649 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 5.47650 | 0.193503 | ||||||||
\(802\) | 23.9748 | 0.846579 | ||||||||
\(803\) | 64.0974 | 2.26195 | ||||||||
\(804\) | 9.03684 | 0.318705 | ||||||||
\(805\) | −1.81163 | −0.0638514 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.4045 | 0.788675 | ||||||||
\(808\) | 8.39612 | 0.295375 | ||||||||
\(809\) | 1.52648 | 0.0536683 | 0.0268341 | − | 0.999640i | \(-0.491457\pi\) | ||||
0.0268341 | + | 0.999640i | \(0.491457\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 51.6039 | 1.81206 | 0.906029 | − | 0.423217i | \(-0.139099\pi\) | ||||
0.906029 | + | 0.423217i | \(0.139099\pi\) | |||||||
\(812\) | −6.97046 | −0.244615 | ||||||||
\(813\) | −23.2325 | −0.814800 | ||||||||
\(814\) | −11.8998 | −0.417087 | ||||||||
\(815\) | 15.1075 | 0.529193 | ||||||||
\(816\) | 2.04892 | 0.0717265 | ||||||||
\(817\) | −14.3448 | −0.501862 | ||||||||
\(818\) | −8.37926 | −0.292974 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.6310 | 0.371251 | ||||||||
\(821\) | −17.4795 | −0.610038 | −0.305019 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305019 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(822\) | −13.1685 | −0.459305 | ||||||||
\(823\) | −25.5566 | −0.890848 | −0.445424 | − | 0.895320i | \(-0.646947\pi\) | ||||
−0.445424 | + | 0.895320i | \(0.646947\pi\) | |||||||
\(824\) | −13.6353 | −0.475009 | ||||||||
\(825\) | −5.29590 | −0.184379 | ||||||||
\(826\) | 18.8605 | 0.656242 | ||||||||
\(827\) | 9.16182 | 0.318588 | 0.159294 | − | 0.987231i | \(-0.449078\pi\) | ||||
0.159294 | + | 0.987231i | \(0.449078\pi\) | |||||||
\(828\) | 1.33513 | 0.0463988 | ||||||||
\(829\) | 48.6493 | 1.68966 | 0.844831 | − | 0.535034i | \(-0.179701\pi\) | ||||
0.844831 | + | 0.535034i | \(0.179701\pi\) | |||||||
\(830\) | −3.02177 | −0.104887 | ||||||||
\(831\) | 9.78448 | 0.339420 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5700 | 0.366230 | ||||||||
\(834\) | 7.17629 | 0.248495 | ||||||||
\(835\) | 16.0881 | 0.556753 | ||||||||
\(836\) | −17.1957 | −0.594725 | ||||||||
\(837\) | 2.80194 | 0.0968491 | ||||||||
\(838\) | −37.0887 | −1.28121 | ||||||||
\(839\) | 8.71246 | 0.300788 | 0.150394 | − | 0.988626i | \(-0.451946\pi\) | ||||
0.150394 | + | 0.988626i | \(0.451946\pi\) | |||||||
\(840\) | −1.35690 | −0.0468174 | ||||||||
\(841\) | −2.61058 | −0.0900200 | ||||||||
\(842\) | 4.90515 | 0.169043 | ||||||||
\(843\) | 21.6286 | 0.744930 | ||||||||
\(844\) | −16.2935 | −0.560846 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.82371 | 0.165842 | ||||||||
\(847\) | 23.1304 | 0.794769 | ||||||||
\(848\) | 14.2349 | 0.488828 | ||||||||
\(849\) | −3.38942 | −0.116325 | ||||||||
\(850\) | 2.04892 | 0.0702773 | ||||||||
\(851\) | 3.00000 | 0.102839 | ||||||||
\(852\) | 11.7506 | 0.402570 | ||||||||
\(853\) | 5.41060 | 0.185255 | 0.0926277 | − | 0.995701i | \(-0.470473\pi\) | ||||
0.0926277 | + | 0.995701i | \(0.470473\pi\) | |||||||
\(854\) | 4.91962 | 0.168346 | ||||||||
\(855\) | 3.24698 | 0.111044 | ||||||||
\(856\) | −3.92394 | −0.134117 | ||||||||
\(857\) | 0.165275 | 0.00564570 | 0.00282285 | − | 0.999996i | \(-0.499101\pi\) | ||||
0.00282285 | + | 0.999996i | \(0.499101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.0853 | 1.60653 | 0.803264 | − | 0.595622i | \(-0.203095\pi\) | ||||
0.803264 | + | 0.595622i | \(0.203095\pi\) | |||||||
\(860\) | −4.41789 | −0.150649 | ||||||||
\(861\) | 14.4252 | 0.491609 | ||||||||
\(862\) | −6.06531 | −0.206585 | ||||||||
\(863\) | 31.2553 | 1.06394 | 0.531972 | − | 0.846762i | \(-0.321451\pi\) | ||||
0.531972 | + | 0.846762i | \(0.321451\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 15.4795 | 0.526318 | ||||||||
\(866\) | 14.8877 | 0.505904 | ||||||||
\(867\) | 12.8019 | 0.434777 | ||||||||
\(868\) | −3.80194 | −0.129046 | ||||||||
\(869\) | 1.37196 | 0.0465406 | ||||||||
\(870\) | 5.13706 | 0.174163 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.554958 | −0.0187933 | ||||||||
\(873\) | 5.85086 | 0.198021 | ||||||||
\(874\) | 4.33513 | 0.146638 | ||||||||
\(875\) | −1.35690 | −0.0458715 | ||||||||
\(876\) | −12.1032 | −0.408930 | ||||||||
\(877\) | −16.9898 | −0.573706 | −0.286853 | − | 0.957975i | \(-0.592609\pi\) | ||||
−0.286853 | + | 0.957975i | \(0.592609\pi\) | |||||||
\(878\) | 21.1336 | 0.713225 | ||||||||
\(879\) | 34.1280 | 1.15111 | ||||||||
\(880\) | −5.29590 | −0.178525 | ||||||||
\(881\) | −3.29159 | −0.110896 | −0.0554482 | − | 0.998462i | \(-0.517659\pi\) | ||||
−0.0554482 | + | 0.998462i | \(0.517659\pi\) | |||||||
\(882\) | 5.15883 | 0.173707 | ||||||||
\(883\) | 17.3157 | 0.582721 | 0.291361 | − | 0.956613i | \(-0.405892\pi\) | ||||
0.291361 | + | 0.956613i | \(0.405892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.8998 | −0.467236 | ||||||||
\(886\) | −28.0683 | −0.942973 | ||||||||
\(887\) | 15.6775 | 0.526401 | 0.263200 | − | 0.964741i | \(-0.415222\pi\) | ||||
0.263200 | + | 0.964741i | \(0.415222\pi\) | |||||||
\(888\) | 2.24698 | 0.0754037 | ||||||||
\(889\) | −3.03252 | −0.101708 | ||||||||
\(890\) | 5.47650 | 0.183573 | ||||||||
\(891\) | 5.29590 | 0.177419 | ||||||||
\(892\) | 2.28083 | 0.0763679 | ||||||||
\(893\) | 15.6625 | 0.524125 | ||||||||
\(894\) | 9.66248 | 0.323162 | ||||||||
\(895\) | −19.0737 | −0.637563 | ||||||||
\(896\) | −1.35690 | −0.0453307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.2446 | 0.642200 | ||||||||
\(899\) | 14.3937 | 0.480058 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −29.1661 | −0.971665 | ||||||||
\(902\) | 56.3008 | 1.87461 | ||||||||
\(903\) | −5.99462 | −0.199489 | ||||||||
\(904\) | −4.39373 | −0.146133 | ||||||||
\(905\) | −2.16852 | −0.0720841 | ||||||||
\(906\) | −7.35152 | −0.244238 | ||||||||
\(907\) | −25.8877 | −0.859587 | −0.429793 | − | 0.902927i | \(-0.641414\pi\) | ||||
−0.429793 | + | 0.902927i | \(0.641414\pi\) | |||||||
\(908\) | 3.37196 | 0.111902 | ||||||||
\(909\) | −8.39612 | −0.278482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5220 | −1.24316 | −0.621579 | − | 0.783351i | \(-0.713509\pi\) | ||||
−0.621579 | + | 0.783351i | \(0.713509\pi\) | |||||||
\(912\) | 3.24698 | 0.107518 | ||||||||
\(913\) | −16.0030 | −0.529621 | ||||||||
\(914\) | −37.8485 | −1.25192 | ||||||||
\(915\) | −3.62565 | −0.119860 | ||||||||
\(916\) | −18.3763 | −0.607169 | ||||||||
\(917\) | −11.5550 | −0.381578 | ||||||||
\(918\) | −2.04892 | −0.0676243 | ||||||||
\(919\) | −5.56358 | −0.183526 | −0.0917628 | − | 0.995781i | \(-0.529250\pi\) | ||||
−0.0917628 | + | 0.995781i | \(0.529250\pi\) | |||||||
\(920\) | 1.33513 | 0.0440178 | ||||||||
\(921\) | −15.6601 | −0.516017 | ||||||||
\(922\) | −11.2228 | −0.369604 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.18598 | −0.236401 | ||||||||
\(925\) | 2.24698 | 0.0738802 | ||||||||
\(926\) | 25.0726 | 0.823937 | ||||||||
\(927\) | 13.6353 | 0.447843 | ||||||||
\(928\) | 5.13706 | 0.168632 | ||||||||
\(929\) | −40.2602 | −1.32090 | −0.660448 | − | 0.750872i | \(-0.729634\pi\) | ||||
−0.660448 | + | 0.750872i | \(0.729634\pi\) | |||||||
\(930\) | 2.80194 | 0.0918792 | ||||||||
\(931\) | 16.7506 | 0.548980 | ||||||||
\(932\) | 10.0858 | 0.330370 | ||||||||
\(933\) | −25.7972 | −0.844561 | ||||||||
\(934\) | −36.9657 | −1.20955 | ||||||||
\(935\) | 10.8509 | 0.354861 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5356 | −0.997554 | −0.498777 | − | 0.866730i | \(-0.666217\pi\) | ||||
−0.498777 | + | 0.866730i | \(0.666217\pi\) | |||||||
\(938\) | 12.2620 | 0.400370 | ||||||||
\(939\) | 15.6243 | 0.509880 | ||||||||
\(940\) | 4.82371 | 0.157332 | ||||||||
\(941\) | 41.6461 | 1.35762 | 0.678812 | − | 0.734312i | \(-0.262495\pi\) | ||||
0.678812 | + | 0.734312i | \(0.262495\pi\) | |||||||
\(942\) | 2.85325 | 0.0929638 | ||||||||
\(943\) | −14.1938 | −0.462212 | ||||||||
\(944\) | −13.8998 | −0.452399 | ||||||||
\(945\) | 1.35690 | 0.0441398 | ||||||||
\(946\) | −23.3967 | −0.760693 | ||||||||
\(947\) | 21.7724 | 0.707508 | 0.353754 | − | 0.935339i | \(-0.384905\pi\) | ||||
0.353754 | + | 0.935339i | \(0.384905\pi\) | |||||||
\(948\) | −0.259061 | −0.00841392 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.24698 | 0.105346 | ||||||||
\(951\) | −9.25965 | −0.300265 | ||||||||
\(952\) | 2.78017 | 0.0901057 | ||||||||
\(953\) | −41.9560 | −1.35909 | −0.679544 | − | 0.733635i | \(-0.737822\pi\) | ||||
−0.679544 | + | 0.733635i | \(0.737822\pi\) | |||||||
\(954\) | −14.2349 | −0.460872 | ||||||||
\(955\) | 11.7409 | 0.379928 | ||||||||
\(956\) | 20.0834 | 0.649542 | ||||||||
\(957\) | 27.2054 | 0.879424 | ||||||||
\(958\) | 31.4590 | 1.01640 | ||||||||
\(959\) | −17.8683 | −0.576998 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −23.1491 | −0.746747 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.92394 | 0.126447 | ||||||||
\(964\) | −2.99462 | −0.0964503 | ||||||||
\(965\) | −24.6722 | −0.794225 | ||||||||
\(966\) | 1.81163 | 0.0582881 | ||||||||
\(967\) | 16.7041 | 0.537168 | 0.268584 | − | 0.963256i | \(-0.413444\pi\) | ||||
0.268584 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(968\) | −17.0465 | −0.547896 | ||||||||
\(969\) | −6.65279 | −0.213718 | ||||||||
\(970\) | 5.85086 | 0.187860 | ||||||||
\(971\) | −20.7275 | −0.665178 | −0.332589 | − | 0.943072i | \(-0.607922\pi\) | ||||
−0.332589 | + | 0.943072i | \(0.607922\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 9.73748 | 0.312169 | ||||||||
\(974\) | 18.8713 | 0.604675 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.62565 | −0.116054 | ||||||||
\(977\) | −33.4547 | −1.07031 | −0.535156 | − | 0.844753i | \(-0.679747\pi\) | ||||
−0.535156 | + | 0.844753i | \(0.679747\pi\) | |||||||
\(978\) | −15.1075 | −0.483085 | ||||||||
\(979\) | 29.0030 | 0.926939 | ||||||||
\(980\) | 5.15883 | 0.164793 | ||||||||
\(981\) | 0.554958 | 0.0177184 | ||||||||
\(982\) | 16.3961 | 0.523221 | ||||||||
\(983\) | 31.8605 | 1.01619 | 0.508097 | − | 0.861300i | \(-0.330349\pi\) | ||||
0.508097 | + | 0.861300i | \(0.330349\pi\) | |||||||
\(984\) | −10.6310 | −0.338905 | ||||||||
\(985\) | 26.2010 | 0.834835 | ||||||||
\(986\) | −10.5254 | −0.335198 | ||||||||
\(987\) | 6.54527 | 0.208338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.89844 | 0.187560 | ||||||||
\(990\) | 5.29590 | 0.168315 | ||||||||
\(991\) | −21.0925 | −0.670024 | −0.335012 | − | 0.942214i | \(-0.608740\pi\) | ||||
−0.335012 | + | 0.942214i | \(0.608740\pi\) | |||||||
\(992\) | 2.80194 | 0.0889616 | ||||||||
\(993\) | 21.8582 | 0.693647 | ||||||||
\(994\) | 15.9444 | 0.505725 | ||||||||
\(995\) | −19.6722 | −0.623650 | ||||||||
\(996\) | 3.02177 | 0.0957485 | ||||||||
\(997\) | 17.7832 | 0.563198 | 0.281599 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281599 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(998\) | 40.2452 | 1.27394 | ||||||||
\(999\) | −2.24698 | −0.0710913 |
(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 | 5070.2.a.bj.1.2 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.t.1351.5 | 6 | |||
13.8 | odd | 4 | 5070.2.b.t.1351.2 | 6 | |||
13.12 | even | 2 | 5070.2.a.bu.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.bu.1.2 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.t.1351.2 | 6 | 13.8 | odd | 4 | |||
5070.2.b.t.1351.5 | 6 | 13.5 | odd | 4 |