Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.85410 | −1.27639 | −0.638197 | − | 0.769873i | \(-0.720319\pi\) | ||||
−0.638197 | + | 0.769873i | \(0.720319\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.85410 | 0.902546 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.85410 | 0.736926 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 7.85410 | 1.90490 | 0.952450 | − | 0.304696i | \(-0.0985548\pi\) | ||||
0.952450 | + | 0.304696i | \(0.0985548\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.61803 | 0.600618 | 0.300309 | − | 0.953842i | \(-0.402910\pi\) | ||||
0.300309 | + | 0.953842i | \(0.402910\pi\) | |||||||
\(20\) | 2.85410 | 0.638197 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.09017 | −0.644345 | −0.322172 | − | 0.946681i | \(-0.604413\pi\) | ||||
−0.322172 | + | 0.946681i | \(0.604413\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | 3.14590 | 0.629180 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | −2.85410 | −0.521085 | ||||||||
\(31\) | −7.32624 | −1.31583 | −0.657916 | − | 0.753092i | \(-0.728562\pi\) | ||||
−0.657916 | + | 0.753092i | \(0.728562\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.85410 | −1.34697 | ||||||||
\(35\) | −2.85410 | −0.482431 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −12.0902 | −1.98761 | −0.993806 | − | 0.111130i | \(-0.964553\pi\) | ||||
−0.993806 | + | 0.111130i | \(0.964553\pi\) | |||||||
\(38\) | −2.61803 | −0.424701 | ||||||||
\(39\) | 1.23607 | 0.197929 | ||||||||
\(40\) | −8.56231 | −1.35382 | ||||||||
\(41\) | −10.8541 | −1.69513 | −0.847563 | − | 0.530695i | \(-0.821931\pi\) | ||||
−0.847563 | + | 0.530695i | \(0.821931\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −1.23607 | −0.188499 | −0.0942493 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942493 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.85410 | −0.425464 | ||||||||
\(46\) | 3.09017 | 0.455621 | ||||||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.14590 | −0.444897 | ||||||||
\(51\) | −7.85410 | −1.09979 | ||||||||
\(52\) | 1.23607 | 0.171412 | ||||||||
\(53\) | 12.1803 | 1.67310 | 0.836549 | − | 0.547892i | \(-0.184569\pi\) | ||||
0.836549 | + | 0.547892i | \(0.184569\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −2.61803 | −0.346767 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 6.76393 | 0.880589 | 0.440294 | − | 0.897853i | \(-0.354874\pi\) | ||||
0.440294 | + | 0.897853i | \(0.354874\pi\) | |||||||
\(60\) | −2.85410 | −0.368463 | ||||||||
\(61\) | 8.94427 | 1.14520 | 0.572598 | − | 0.819836i | \(-0.305935\pi\) | ||||
0.572598 | + | 0.819836i | \(0.305935\pi\) | |||||||
\(62\) | 7.32624 | 0.930433 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 3.52786 | 0.437578 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | −7.85410 | −0.952450 | ||||||||
\(69\) | 3.09017 | 0.372013 | ||||||||
\(70\) | 2.85410 | 0.341130 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −5.23607 | −0.612835 | −0.306418 | − | 0.951897i | \(-0.599130\pi\) | ||||
−0.306418 | + | 0.951897i | \(0.599130\pi\) | |||||||
\(74\) | 12.0902 | 1.40545 | ||||||||
\(75\) | −3.14590 | −0.363257 | ||||||||
\(76\) | −2.61803 | −0.300309 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.23607 | −0.139957 | ||||||||
\(79\) | −14.0000 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 2.85410 | 0.319098 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.8541 | 1.19864 | ||||||||
\(83\) | 2.94427 | 0.323176 | 0.161588 | − | 0.986858i | \(-0.448338\pi\) | ||||
0.161588 | + | 0.986858i | \(0.448338\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −22.4164 | −2.43140 | ||||||||
\(86\) | 1.23607 | 0.133289 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.09017 | 0.115558 | 0.0577789 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577789 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(90\) | 2.85410 | 0.300849 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | 3.09017 | 0.322172 | ||||||||
\(93\) | 7.32624 | 0.759695 | ||||||||
\(94\) | −2.00000 | −0.206284 | ||||||||
\(95\) | −7.47214 | −0.766625 | ||||||||
\(96\) | 5.00000 | 0.510310 | ||||||||
\(97\) | −3.52786 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.14590 | −0.314590 | ||||||||
\(101\) | −2.09017 | −0.207980 | −0.103990 | − | 0.994578i | \(-0.533161\pi\) | ||||
−0.103990 | + | 0.994578i | \(0.533161\pi\) | |||||||
\(102\) | 7.85410 | 0.777672 | ||||||||
\(103\) | −10.3262 | −1.01747 | −0.508737 | − | 0.860922i | \(-0.669888\pi\) | ||||
−0.508737 | + | 0.860922i | \(0.669888\pi\) | |||||||
\(104\) | −3.70820 | −0.363619 | ||||||||
\(105\) | 2.85410 | 0.278532 | ||||||||
\(106\) | −12.1803 | −1.18306 | ||||||||
\(107\) | 4.90983 | 0.474651 | 0.237326 | − | 0.971430i | \(-0.423729\pi\) | ||||
0.237326 | + | 0.971430i | \(0.423729\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.5623 | 1.01169 | 0.505843 | − | 0.862626i | \(-0.331182\pi\) | ||||
0.505843 | + | 0.862626i | \(0.331182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0902 | 1.14755 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 0.763932 | 0.0718647 | 0.0359323 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359323 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(114\) | 2.61803 | 0.245201 | ||||||||
\(115\) | 8.81966 | 0.822438 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | −1.23607 | −0.114275 | ||||||||
\(118\) | −6.76393 | −0.622670 | ||||||||
\(119\) | 7.85410 | 0.719984 | ||||||||
\(120\) | 8.56231 | 0.781628 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.94427 | −0.809776 | ||||||||
\(123\) | 10.8541 | 0.978681 | ||||||||
\(124\) | 7.32624 | 0.657916 | ||||||||
\(125\) | 5.29180 | 0.473313 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −3.23607 | −0.287155 | −0.143577 | − | 0.989639i | \(-0.545861\pi\) | ||||
−0.143577 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 1.23607 | 0.108830 | ||||||||
\(130\) | −3.52786 | −0.309414 | ||||||||
\(131\) | 2.29180 | 0.200235 | 0.100118 | − | 0.994976i | \(-0.468078\pi\) | ||||
0.100118 | + | 0.994976i | \(0.468078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.61803 | 0.227012 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 2.85410 | 0.245642 | ||||||||
\(136\) | 23.5623 | 2.02045 | ||||||||
\(137\) | 6.76393 | 0.577882 | 0.288941 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288941 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(138\) | −3.09017 | −0.263053 | ||||||||
\(139\) | 4.79837 | 0.406993 | 0.203496 | − | 0.979076i | \(-0.434769\pi\) | ||||
0.203496 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(140\) | 2.85410 | 0.241216 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | −8.94427 | −0.750587 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 5.70820 | 0.474041 | ||||||||
\(146\) | 5.23607 | 0.433340 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 12.0902 | 0.993806 | ||||||||
\(149\) | −20.0000 | −1.63846 | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 3.14590 | 0.256861 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 7.85410 | 0.637052 | ||||||||
\(153\) | 7.85410 | 0.634967 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.9098 | 1.67952 | ||||||||
\(156\) | −1.23607 | −0.0989646 | ||||||||
\(157\) | 9.70820 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(158\) | 14.0000 | 1.11378 | ||||||||
\(159\) | −12.1803 | −0.965964 | ||||||||
\(160\) | 14.2705 | 1.12818 | ||||||||
\(161\) | −3.09017 | −0.243540 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.41641 | −0.424246 | −0.212123 | − | 0.977243i | \(-0.568038\pi\) | ||||
−0.212123 | + | 0.977243i | \(0.568038\pi\) | |||||||
\(164\) | 10.8541 | 0.847563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.94427 | −0.228520 | ||||||||
\(167\) | 8.18034 | 0.633014 | 0.316507 | − | 0.948590i | \(-0.397490\pi\) | ||||
0.316507 | + | 0.948590i | \(0.397490\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 22.4164 | 1.71926 | ||||||||
\(171\) | 2.61803 | 0.200206 | ||||||||
\(172\) | 1.23607 | 0.0942493 | ||||||||
\(173\) | 19.8541 | 1.50948 | 0.754740 | − | 0.656024i | \(-0.227763\pi\) | ||||
0.754740 | + | 0.656024i | \(0.227763\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 3.14590 | 0.237808 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.76393 | −0.508408 | ||||||||
\(178\) | −1.09017 | −0.0817117 | ||||||||
\(179\) | 8.38197 | 0.626498 | 0.313249 | − | 0.949671i | \(-0.398583\pi\) | ||||
0.313249 | + | 0.949671i | \(0.398583\pi\) | |||||||
\(180\) | 2.85410 | 0.212732 | ||||||||
\(181\) | −18.9443 | −1.40812 | −0.704058 | − | 0.710142i | \(-0.748631\pi\) | ||||
−0.704058 | + | 0.710142i | \(0.748631\pi\) | |||||||
\(182\) | 1.23607 | 0.0916235 | ||||||||
\(183\) | −8.94427 | −0.661180 | ||||||||
\(184\) | −9.27051 | −0.683431 | ||||||||
\(185\) | 34.5066 | 2.53697 | ||||||||
\(186\) | −7.32624 | −0.537186 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 7.47214 | 0.542086 | ||||||||
\(191\) | −18.2705 | −1.32201 | −0.661004 | − | 0.750383i | \(-0.729869\pi\) | ||||
−0.661004 | + | 0.750383i | \(0.729869\pi\) | |||||||
\(192\) | −7.00000 | −0.505181 | ||||||||
\(193\) | 18.3820 | 1.32316 | 0.661581 | − | 0.749873i | \(-0.269886\pi\) | ||||
0.661581 | + | 0.749873i | \(0.269886\pi\) | |||||||
\(194\) | 3.52786 | 0.253286 | ||||||||
\(195\) | −3.52786 | −0.252636 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.61803 | −0.185588 | −0.0927938 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927938 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(200\) | 9.43769 | 0.667346 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 2.09017 | 0.147064 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 7.85410 | 0.549897 | ||||||||
\(205\) | 30.9787 | 2.16365 | ||||||||
\(206\) | 10.3262 | 0.719463 | ||||||||
\(207\) | −3.09017 | −0.214782 | ||||||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.85410 | −0.196952 | ||||||||
\(211\) | −2.00000 | −0.137686 | −0.0688428 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688428 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(212\) | −12.1803 | −0.836549 | ||||||||
\(213\) | −8.94427 | −0.612851 | ||||||||
\(214\) | −4.90983 | −0.335629 | ||||||||
\(215\) | 3.52786 | 0.240598 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | −7.32624 | −0.497337 | ||||||||
\(218\) | −10.5623 | −0.715370 | ||||||||
\(219\) | 5.23607 | 0.353821 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.70820 | −0.653044 | ||||||||
\(222\) | −12.0902 | −0.811439 | ||||||||
\(223\) | 20.7984 | 1.39276 | 0.696381 | − | 0.717672i | \(-0.254792\pi\) | ||||
0.696381 | + | 0.717672i | \(0.254792\pi\) | |||||||
\(224\) | −5.00000 | −0.334077 | ||||||||
\(225\) | 3.14590 | 0.209727 | ||||||||
\(226\) | −0.763932 | −0.0508160 | ||||||||
\(227\) | 21.4164 | 1.42146 | 0.710728 | − | 0.703466i | \(-0.248365\pi\) | ||||
0.710728 | + | 0.703466i | \(0.248365\pi\) | |||||||
\(228\) | 2.61803 | 0.173384 | ||||||||
\(229\) | 21.2361 | 1.40332 | 0.701659 | − | 0.712512i | \(-0.252443\pi\) | ||||
0.701659 | + | 0.712512i | \(0.252443\pi\) | |||||||
\(230\) | −8.81966 | −0.581551 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −5.70820 | −0.373957 | −0.186978 | − | 0.982364i | \(-0.559869\pi\) | ||||
−0.186978 | + | 0.982364i | \(0.559869\pi\) | |||||||
\(234\) | 1.23607 | 0.0808043 | ||||||||
\(235\) | −5.70820 | −0.372362 | ||||||||
\(236\) | −6.76393 | −0.440294 | ||||||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | −7.85410 | −0.509106 | ||||||||
\(239\) | −1.56231 | −0.101057 | −0.0505286 | − | 0.998723i | \(-0.516091\pi\) | ||||
−0.0505286 | + | 0.998723i | \(0.516091\pi\) | |||||||
\(240\) | −2.85410 | −0.184231 | ||||||||
\(241\) | 4.94427 | 0.318489 | 0.159244 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159244 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.94427 | −0.572598 | ||||||||
\(245\) | −2.85410 | −0.182342 | ||||||||
\(246\) | −10.8541 | −0.692032 | ||||||||
\(247\) | −3.23607 | −0.205906 | ||||||||
\(248\) | −21.9787 | −1.39565 | ||||||||
\(249\) | −2.94427 | −0.186586 | ||||||||
\(250\) | −5.29180 | −0.334683 | ||||||||
\(251\) | 24.1803 | 1.52625 | 0.763125 | − | 0.646251i | \(-0.223664\pi\) | ||||
0.763125 | + | 0.646251i | \(0.223664\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.23607 | 0.203049 | ||||||||
\(255\) | 22.4164 | 1.40377 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 2.61803 | 0.163308 | 0.0816542 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816542 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(258\) | −1.23607 | −0.0769542 | ||||||||
\(259\) | −12.0902 | −0.751247 | ||||||||
\(260\) | −3.52786 | −0.218789 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | −2.29180 | −0.141588 | ||||||||
\(263\) | 2.43769 | 0.150315 | 0.0751573 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751573 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.7639 | −2.13553 | ||||||||
\(266\) | −2.61803 | −0.160522 | ||||||||
\(267\) | −1.09017 | −0.0667173 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | 27.8885 | 1.70039 | 0.850197 | − | 0.526464i | \(-0.176483\pi\) | ||||
0.850197 | + | 0.526464i | \(0.176483\pi\) | |||||||
\(270\) | −2.85410 | −0.173695 | ||||||||
\(271\) | 24.0902 | 1.46337 | 0.731687 | − | 0.681641i | \(-0.238733\pi\) | ||||
0.731687 | + | 0.681641i | \(0.238733\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | 1.23607 | 0.0748102 | ||||||||
\(274\) | −6.76393 | −0.408624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.09017 | −0.186006 | ||||||||
\(277\) | −10.4377 | −0.627140 | −0.313570 | − | 0.949565i | \(-0.601525\pi\) | ||||
−0.313570 | + | 0.949565i | \(0.601525\pi\) | |||||||
\(278\) | −4.79837 | −0.287787 | ||||||||
\(279\) | −7.32624 | −0.438610 | ||||||||
\(280\) | −8.56231 | −0.511696 | ||||||||
\(281\) | 1.05573 | 0.0629795 | 0.0314897 | − | 0.999504i | \(-0.489975\pi\) | ||||
0.0314897 | + | 0.999504i | \(0.489975\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 13.4377 | 0.798788 | 0.399394 | − | 0.916779i | \(-0.369221\pi\) | ||||
0.399394 | + | 0.916779i | \(0.369221\pi\) | |||||||
\(284\) | −8.94427 | −0.530745 | ||||||||
\(285\) | 7.47214 | 0.442611 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8541 | −0.640697 | ||||||||
\(288\) | −5.00000 | −0.294628 | ||||||||
\(289\) | 44.6869 | 2.62864 | ||||||||
\(290\) | −5.70820 | −0.335197 | ||||||||
\(291\) | 3.52786 | 0.206807 | ||||||||
\(292\) | 5.23607 | 0.306418 | ||||||||
\(293\) | 19.7984 | 1.15663 | 0.578317 | − | 0.815812i | \(-0.303710\pi\) | ||||
0.578317 | + | 0.815812i | \(0.303710\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −19.3050 | −1.12398 | ||||||||
\(296\) | −36.2705 | −2.10818 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0000 | 1.15857 | ||||||||
\(299\) | 3.81966 | 0.220897 | ||||||||
\(300\) | 3.14590 | 0.181629 | ||||||||
\(301\) | −1.23607 | −0.0712458 | ||||||||
\(302\) | 2.00000 | 0.115087 | ||||||||
\(303\) | 2.09017 | 0.120077 | ||||||||
\(304\) | −2.61803 | −0.150155 | ||||||||
\(305\) | −25.5279 | −1.46172 | ||||||||
\(306\) | −7.85410 | −0.448989 | ||||||||
\(307\) | −24.2705 | −1.38519 | −0.692596 | − | 0.721326i | \(-0.743533\pi\) | ||||
−0.692596 | + | 0.721326i | \(0.743533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3262 | 0.587439 | ||||||||
\(310\) | −20.9098 | −1.18760 | ||||||||
\(311\) | −0.763932 | −0.0433186 | −0.0216593 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216593 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(312\) | 3.70820 | 0.209936 | ||||||||
\(313\) | −9.81966 | −0.555040 | −0.277520 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277520 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(314\) | −9.70820 | −0.547866 | ||||||||
\(315\) | −2.85410 | −0.160810 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | −27.5967 | −1.54999 | −0.774994 | − | 0.631969i | \(-0.782247\pi\) | ||||
−0.774994 | + | 0.631969i | \(0.782247\pi\) | |||||||
\(318\) | 12.1803 | 0.683040 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −19.9787 | −1.11684 | ||||||||
\(321\) | −4.90983 | −0.274040 | ||||||||
\(322\) | 3.09017 | 0.172208 | ||||||||
\(323\) | 20.5623 | 1.14412 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −3.88854 | −0.215698 | ||||||||
\(326\) | 5.41641 | 0.299987 | ||||||||
\(327\) | −10.5623 | −0.584097 | ||||||||
\(328\) | −32.5623 | −1.79795 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3607 | 1.66877 | 0.834387 | − | 0.551179i | \(-0.185822\pi\) | ||||
0.834387 | + | 0.551179i | \(0.185822\pi\) | |||||||
\(332\) | −2.94427 | −0.161588 | ||||||||
\(333\) | −12.0902 | −0.662537 | ||||||||
\(334\) | −8.18034 | −0.447608 | ||||||||
\(335\) | −22.8328 | −1.24749 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −27.1459 | −1.47873 | −0.739366 | − | 0.673304i | \(-0.764874\pi\) | ||||
−0.739366 | + | 0.673304i | \(0.764874\pi\) | |||||||
\(338\) | 11.4721 | 0.624002 | ||||||||
\(339\) | −0.763932 | −0.0414911 | ||||||||
\(340\) | 22.4164 | 1.21570 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.61803 | −0.141567 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.70820 | −0.199933 | ||||||||
\(345\) | −8.81966 | −0.474835 | ||||||||
\(346\) | −19.8541 | −1.06736 | ||||||||
\(347\) | −12.3820 | −0.664699 | −0.332349 | − | 0.943156i | \(-0.607841\pi\) | ||||
−0.332349 | + | 0.943156i | \(0.607841\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | 22.7639 | 1.21853 | 0.609263 | − | 0.792968i | \(-0.291466\pi\) | ||||
0.609263 | + | 0.792968i | \(0.291466\pi\) | |||||||
\(350\) | −3.14590 | −0.168155 | ||||||||
\(351\) | 1.23607 | 0.0659764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.4721 | 0.663825 | 0.331912 | − | 0.943310i | \(-0.392306\pi\) | ||||
0.331912 | + | 0.943310i | \(0.392306\pi\) | |||||||
\(354\) | 6.76393 | 0.359499 | ||||||||
\(355\) | −25.5279 | −1.35488 | ||||||||
\(356\) | −1.09017 | −0.0577789 | ||||||||
\(357\) | −7.85410 | −0.415683 | ||||||||
\(358\) | −8.38197 | −0.443001 | ||||||||
\(359\) | 7.03444 | 0.371264 | 0.185632 | − | 0.982619i | \(-0.440567\pi\) | ||||
0.185632 | + | 0.982619i | \(0.440567\pi\) | |||||||
\(360\) | −8.56231 | −0.451273 | ||||||||
\(361\) | −12.1459 | −0.639258 | ||||||||
\(362\) | 18.9443 | 0.995689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.23607 | 0.0647876 | ||||||||
\(365\) | 14.9443 | 0.782219 | ||||||||
\(366\) | 8.94427 | 0.467525 | ||||||||
\(367\) | 16.2705 | 0.849314 | 0.424657 | − | 0.905354i | \(-0.360395\pi\) | ||||
0.424657 | + | 0.905354i | \(0.360395\pi\) | |||||||
\(368\) | 3.09017 | 0.161086 | ||||||||
\(369\) | −10.8541 | −0.565042 | ||||||||
\(370\) | −34.5066 | −1.79391 | ||||||||
\(371\) | 12.1803 | 0.632372 | ||||||||
\(372\) | −7.32624 | −0.379848 | ||||||||
\(373\) | −23.3262 | −1.20779 | −0.603893 | − | 0.797065i | \(-0.706385\pi\) | ||||
−0.603893 | + | 0.797065i | \(0.706385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.29180 | −0.273267 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 2.47214 | 0.127321 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 2.47214 | 0.126985 | 0.0634925 | − | 0.997982i | \(-0.479776\pi\) | ||||
0.0634925 | + | 0.997982i | \(0.479776\pi\) | |||||||
\(380\) | 7.47214 | 0.383312 | ||||||||
\(381\) | 3.23607 | 0.165789 | ||||||||
\(382\) | 18.2705 | 0.934801 | ||||||||
\(383\) | −13.0557 | −0.667117 | −0.333558 | − | 0.942729i | \(-0.608249\pi\) | ||||
−0.333558 | + | 0.942729i | \(0.608249\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.3820 | −0.935617 | ||||||||
\(387\) | −1.23607 | −0.0628329 | ||||||||
\(388\) | 3.52786 | 0.179100 | ||||||||
\(389\) | 22.1803 | 1.12459 | 0.562294 | − | 0.826937i | \(-0.309919\pi\) | ||||
0.562294 | + | 0.826937i | \(0.309919\pi\) | |||||||
\(390\) | 3.52786 | 0.178640 | ||||||||
\(391\) | −24.2705 | −1.22741 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | −2.29180 | −0.115606 | ||||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | 39.9574 | 2.01048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6525 | 0.735387 | 0.367693 | − | 0.929947i | \(-0.380148\pi\) | ||||
0.367693 | + | 0.929947i | \(0.380148\pi\) | |||||||
\(398\) | 2.61803 | 0.131230 | ||||||||
\(399\) | −2.61803 | −0.131066 | ||||||||
\(400\) | −3.14590 | −0.157295 | ||||||||
\(401\) | 18.4721 | 0.922454 | 0.461227 | − | 0.887282i | \(-0.347409\pi\) | ||||
0.461227 | + | 0.887282i | \(0.347409\pi\) | |||||||
\(402\) | 8.00000 | 0.399004 | ||||||||
\(403\) | 9.05573 | 0.451098 | ||||||||
\(404\) | 2.09017 | 0.103990 | ||||||||
\(405\) | −2.85410 | −0.141821 | ||||||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −23.5623 | −1.16651 | ||||||||
\(409\) | 28.7639 | 1.42228 | 0.711142 | − | 0.703048i | \(-0.248178\pi\) | ||||
0.711142 | + | 0.703048i | \(0.248178\pi\) | |||||||
\(410\) | −30.9787 | −1.52993 | ||||||||
\(411\) | −6.76393 | −0.333640 | ||||||||
\(412\) | 10.3262 | 0.508737 | ||||||||
\(413\) | 6.76393 | 0.332831 | ||||||||
\(414\) | 3.09017 | 0.151874 | ||||||||
\(415\) | −8.40325 | −0.412499 | ||||||||
\(416\) | 6.18034 | 0.303016 | ||||||||
\(417\) | −4.79837 | −0.234977 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7639 | 0.721265 | 0.360633 | − | 0.932708i | \(-0.382561\pi\) | ||||
0.360633 | + | 0.932708i | \(0.382561\pi\) | |||||||
\(420\) | −2.85410 | −0.139266 | ||||||||
\(421\) | −4.32624 | −0.210848 | −0.105424 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105424 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(422\) | 2.00000 | 0.0973585 | ||||||||
\(423\) | 2.00000 | 0.0972433 | ||||||||
\(424\) | 36.5410 | 1.77459 | ||||||||
\(425\) | 24.7082 | 1.19852 | ||||||||
\(426\) | 8.94427 | 0.433351 | ||||||||
\(427\) | 8.94427 | 0.432844 | ||||||||
\(428\) | −4.90983 | −0.237326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.52786 | −0.170129 | ||||||||
\(431\) | −2.09017 | −0.100680 | −0.0503400 | − | 0.998732i | \(-0.516030\pi\) | ||||
−0.0503400 | + | 0.998732i | \(0.516030\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.2361 | −0.828313 | −0.414156 | − | 0.910206i | \(-0.635923\pi\) | ||||
−0.414156 | + | 0.910206i | \(0.635923\pi\) | |||||||
\(434\) | 7.32624 | 0.351671 | ||||||||
\(435\) | −5.70820 | −0.273687 | ||||||||
\(436\) | −10.5623 | −0.505843 | ||||||||
\(437\) | −8.09017 | −0.387005 | ||||||||
\(438\) | −5.23607 | −0.250189 | ||||||||
\(439\) | −21.7984 | −1.04038 | −0.520190 | − | 0.854051i | \(-0.674139\pi\) | ||||
−0.520190 | + | 0.854051i | \(0.674139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 9.70820 | 0.461772 | ||||||||
\(443\) | 4.90983 | 0.233273 | 0.116637 | − | 0.993175i | \(-0.462789\pi\) | ||||
0.116637 | + | 0.993175i | \(0.462789\pi\) | |||||||
\(444\) | −12.0902 | −0.573774 | ||||||||
\(445\) | −3.11146 | −0.147497 | ||||||||
\(446\) | −20.7984 | −0.984832 | ||||||||
\(447\) | 20.0000 | 0.945968 | ||||||||
\(448\) | 7.00000 | 0.330719 | ||||||||
\(449\) | 41.8885 | 1.97684 | 0.988421 | − | 0.151734i | \(-0.0484858\pi\) | ||||
0.988421 | + | 0.151734i | \(0.0484858\pi\) | |||||||
\(450\) | −3.14590 | −0.148299 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.763932 | −0.0359323 | ||||||||
\(453\) | 2.00000 | 0.0939682 | ||||||||
\(454\) | −21.4164 | −1.00512 | ||||||||
\(455\) | 3.52786 | 0.165389 | ||||||||
\(456\) | −7.85410 | −0.367802 | ||||||||
\(457\) | 12.4721 | 0.583422 | 0.291711 | − | 0.956507i | \(-0.405775\pi\) | ||||
0.291711 | + | 0.956507i | \(0.405775\pi\) | |||||||
\(458\) | −21.2361 | −0.992296 | ||||||||
\(459\) | −7.85410 | −0.366598 | ||||||||
\(460\) | −8.81966 | −0.411219 | ||||||||
\(461\) | −6.36068 | −0.296246 | −0.148123 | − | 0.988969i | \(-0.547323\pi\) | ||||
−0.148123 | + | 0.988969i | \(0.547323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4164 | 0.530565 | 0.265283 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265283 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | −20.9098 | −0.969670 | ||||||||
\(466\) | 5.70820 | 0.264427 | ||||||||
\(467\) | 19.2361 | 0.890139 | 0.445070 | − | 0.895496i | \(-0.353179\pi\) | ||||
0.445070 | + | 0.895496i | \(0.353179\pi\) | |||||||
\(468\) | 1.23607 | 0.0571373 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 5.70820 | 0.263300 | ||||||||
\(471\) | −9.70820 | −0.447330 | ||||||||
\(472\) | 20.2918 | 0.934006 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −14.0000 | −0.643041 | ||||||||
\(475\) | 8.23607 | 0.377897 | ||||||||
\(476\) | −7.85410 | −0.359992 | ||||||||
\(477\) | 12.1803 | 0.557699 | ||||||||
\(478\) | 1.56231 | 0.0714582 | ||||||||
\(479\) | −11.0557 | −0.505149 | −0.252575 | − | 0.967577i | \(-0.581277\pi\) | ||||
−0.252575 | + | 0.967577i | \(0.581277\pi\) | |||||||
\(480\) | −14.2705 | −0.651357 | ||||||||
\(481\) | 14.9443 | 0.681400 | ||||||||
\(482\) | −4.94427 | −0.225205 | ||||||||
\(483\) | 3.09017 | 0.140608 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0689 | 0.457204 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −39.2361 | −1.77796 | −0.888978 | − | 0.457950i | \(-0.848584\pi\) | ||||
−0.888978 | + | 0.457950i | \(0.848584\pi\) | |||||||
\(488\) | 26.8328 | 1.21466 | ||||||||
\(489\) | 5.41641 | 0.244938 | ||||||||
\(490\) | 2.85410 | 0.128935 | ||||||||
\(491\) | −0.326238 | −0.0147229 | −0.00736146 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736146 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(492\) | −10.8541 | −0.489341 | ||||||||
\(493\) | −15.7082 | −0.707462 | ||||||||
\(494\) | 3.23607 | 0.145598 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.32624 | 0.328958 | ||||||||
\(497\) | 8.94427 | 0.401205 | ||||||||
\(498\) | 2.94427 | 0.131936 | ||||||||
\(499\) | 26.1803 | 1.17199 | 0.585996 | − | 0.810314i | \(-0.300703\pi\) | ||||
0.585996 | + | 0.810314i | \(0.300703\pi\) | |||||||
\(500\) | −5.29180 | −0.236656 | ||||||||
\(501\) | −8.18034 | −0.365471 | ||||||||
\(502\) | −24.1803 | −1.07922 | ||||||||
\(503\) | −0.583592 | −0.0260211 | −0.0130105 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130105 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 5.96556 | 0.265464 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | 3.23607 | 0.143577 | ||||||||
\(509\) | −5.90983 | −0.261949 | −0.130974 | − | 0.991386i | \(-0.541811\pi\) | ||||
−0.130974 | + | 0.991386i | \(0.541811\pi\) | |||||||
\(510\) | −22.4164 | −0.992615 | ||||||||
\(511\) | −5.23607 | −0.231630 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −2.61803 | −0.115589 | ||||||||
\(514\) | −2.61803 | −0.115477 | ||||||||
\(515\) | 29.4721 | 1.29870 | ||||||||
\(516\) | −1.23607 | −0.0544149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.0902 | 0.531212 | ||||||||
\(519\) | −19.8541 | −0.871498 | ||||||||
\(520\) | 10.5836 | 0.464121 | ||||||||
\(521\) | −11.6180 | −0.508995 | −0.254498 | − | 0.967073i | \(-0.581910\pi\) | ||||
−0.254498 | + | 0.967073i | \(0.581910\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 2.90983 | 0.127238 | 0.0636190 | − | 0.997974i | \(-0.479736\pi\) | ||||
0.0636190 | + | 0.997974i | \(0.479736\pi\) | |||||||
\(524\) | −2.29180 | −0.100118 | ||||||||
\(525\) | −3.14590 | −0.137298 | ||||||||
\(526\) | −2.43769 | −0.106289 | ||||||||
\(527\) | −57.5410 | −2.50653 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.4508 | −0.584820 | ||||||||
\(530\) | 34.7639 | 1.51005 | ||||||||
\(531\) | 6.76393 | 0.293530 | ||||||||
\(532\) | −2.61803 | −0.113506 | ||||||||
\(533\) | 13.4164 | 0.581129 | ||||||||
\(534\) | 1.09017 | 0.0471763 | ||||||||
\(535\) | −14.0132 | −0.605842 | ||||||||
\(536\) | 24.0000 | 1.03664 | ||||||||
\(537\) | −8.38197 | −0.361709 | ||||||||
\(538\) | −27.8885 | −1.20236 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.85410 | −0.122821 | ||||||||
\(541\) | 16.8541 | 0.724614 | 0.362307 | − | 0.932059i | \(-0.381989\pi\) | ||||
0.362307 | + | 0.932059i | \(0.381989\pi\) | |||||||
\(542\) | −24.0902 | −1.03476 | ||||||||
\(543\) | 18.9443 | 0.812977 | ||||||||
\(544\) | −39.2705 | −1.68371 | ||||||||
\(545\) | −30.1459 | −1.29131 | ||||||||
\(546\) | −1.23607 | −0.0528988 | ||||||||
\(547\) | −36.4721 | −1.55944 | −0.779718 | − | 0.626131i | \(-0.784638\pi\) | ||||
−0.779718 | + | 0.626131i | \(0.784638\pi\) | |||||||
\(548\) | −6.76393 | −0.288941 | ||||||||
\(549\) | 8.94427 | 0.381732 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.23607 | −0.223064 | ||||||||
\(552\) | 9.27051 | 0.394579 | ||||||||
\(553\) | −14.0000 | −0.595341 | ||||||||
\(554\) | 10.4377 | 0.443455 | ||||||||
\(555\) | −34.5066 | −1.46472 | ||||||||
\(556\) | −4.79837 | −0.203496 | ||||||||
\(557\) | −21.4164 | −0.907442 | −0.453721 | − | 0.891144i | \(-0.649904\pi\) | ||||
−0.453721 | + | 0.891144i | \(0.649904\pi\) | |||||||
\(558\) | 7.32624 | 0.310144 | ||||||||
\(559\) | 1.52786 | 0.0646218 | ||||||||
\(560\) | 2.85410 | 0.120608 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.05573 | −0.0445332 | ||||||||
\(563\) | 40.3607 | 1.70100 | 0.850500 | − | 0.525975i | \(-0.176300\pi\) | ||||
0.850500 | + | 0.525975i | \(0.176300\pi\) | |||||||
\(564\) | 2.00000 | 0.0842152 | ||||||||
\(565\) | −2.18034 | −0.0917276 | ||||||||
\(566\) | −13.4377 | −0.564828 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 26.8328 | 1.12588 | ||||||||
\(569\) | −18.1803 | −0.762159 | −0.381080 | − | 0.924542i | \(-0.624448\pi\) | ||||
−0.381080 | + | 0.924542i | \(0.624448\pi\) | |||||||
\(570\) | −7.47214 | −0.312973 | ||||||||
\(571\) | 28.5410 | 1.19440 | 0.597202 | − | 0.802091i | \(-0.296279\pi\) | ||||
0.597202 | + | 0.802091i | \(0.296279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.2705 | 0.763261 | ||||||||
\(574\) | 10.8541 | 0.453041 | ||||||||
\(575\) | −9.72136 | −0.405409 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −14.6525 | −0.609991 | −0.304995 | − | 0.952354i | \(-0.598655\pi\) | ||||
−0.304995 | + | 0.952354i | \(0.598655\pi\) | |||||||
\(578\) | −44.6869 | −1.85873 | ||||||||
\(579\) | −18.3820 | −0.763928 | ||||||||
\(580\) | −5.70820 | −0.237020 | ||||||||
\(581\) | 2.94427 | 0.122149 | ||||||||
\(582\) | −3.52786 | −0.146235 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.7082 | −0.650010 | ||||||||
\(585\) | 3.52786 | 0.145859 | ||||||||
\(586\) | −19.7984 | −0.817863 | ||||||||
\(587\) | 3.88854 | 0.160497 | 0.0802487 | − | 0.996775i | \(-0.474429\pi\) | ||||
0.0802487 | + | 0.996775i | \(0.474429\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −19.1803 | −0.790312 | ||||||||
\(590\) | 19.3050 | 0.794772 | ||||||||
\(591\) | −4.00000 | −0.164538 | ||||||||
\(592\) | 12.0902 | 0.496903 | ||||||||
\(593\) | 3.43769 | 0.141169 | 0.0705846 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705846 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.4164 | −0.918983 | ||||||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 2.61803 | 0.107149 | ||||||||
\(598\) | −3.81966 | −0.156198 | ||||||||
\(599\) | −1.56231 | −0.0638341 | −0.0319170 | − | 0.999491i | \(-0.510161\pi\) | ||||
−0.0319170 | + | 0.999491i | \(0.510161\pi\) | |||||||
\(600\) | −9.43769 | −0.385292 | ||||||||
\(601\) | 6.00000 | 0.244745 | 0.122373 | − | 0.992484i | \(-0.460950\pi\) | ||||
0.122373 | + | 0.992484i | \(0.460950\pi\) | |||||||
\(602\) | 1.23607 | 0.0503784 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.09017 | −0.0849073 | ||||||||
\(607\) | −10.3262 | −0.419129 | −0.209565 | − | 0.977795i | \(-0.567205\pi\) | ||||
−0.209565 | + | 0.977795i | \(0.567205\pi\) | |||||||
\(608\) | −13.0902 | −0.530876 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 25.5279 | 1.03359 | ||||||||
\(611\) | −2.47214 | −0.100012 | ||||||||
\(612\) | −7.85410 | −0.317483 | ||||||||
\(613\) | −5.85410 | −0.236445 | −0.118222 | − | 0.992987i | \(-0.537720\pi\) | ||||
−0.118222 | + | 0.992987i | \(0.537720\pi\) | |||||||
\(614\) | 24.2705 | 0.979478 | ||||||||
\(615\) | −30.9787 | −1.24918 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.6525 | 1.79764 | 0.898820 | − | 0.438317i | \(-0.144425\pi\) | ||||
0.898820 | + | 0.438317i | \(0.144425\pi\) | |||||||
\(618\) | −10.3262 | −0.415382 | ||||||||
\(619\) | −11.5066 | −0.462488 | −0.231244 | − | 0.972896i | \(-0.574280\pi\) | ||||
−0.231244 | + | 0.972896i | \(0.574280\pi\) | |||||||
\(620\) | −20.9098 | −0.839759 | ||||||||
\(621\) | 3.09017 | 0.124004 | ||||||||
\(622\) | 0.763932 | 0.0306309 | ||||||||
\(623\) | 1.09017 | 0.0436767 | ||||||||
\(624\) | −1.23607 | −0.0494823 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 9.81966 | 0.392473 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.70820 | −0.387400 | ||||||||
\(629\) | −94.9574 | −3.78620 | ||||||||
\(630\) | 2.85410 | 0.113710 | ||||||||
\(631\) | 29.8885 | 1.18984 | 0.594922 | − | 0.803783i | \(-0.297183\pi\) | ||||
0.594922 | + | 0.803783i | \(0.297183\pi\) | |||||||
\(632\) | −42.0000 | −1.67067 | ||||||||
\(633\) | 2.00000 | 0.0794929 | ||||||||
\(634\) | 27.5967 | 1.09601 | ||||||||
\(635\) | 9.23607 | 0.366522 | ||||||||
\(636\) | 12.1803 | 0.482982 | ||||||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.94427 | 0.353830 | ||||||||
\(640\) | −8.56231 | −0.338455 | ||||||||
\(641\) | 8.65248 | 0.341752 | 0.170876 | − | 0.985293i | \(-0.445340\pi\) | ||||
0.170876 | + | 0.985293i | \(0.445340\pi\) | |||||||
\(642\) | 4.90983 | 0.193776 | ||||||||
\(643\) | 47.9230 | 1.88990 | 0.944949 | − | 0.327218i | \(-0.106111\pi\) | ||||
0.944949 | + | 0.327218i | \(0.106111\pi\) | |||||||
\(644\) | 3.09017 | 0.121770 | ||||||||
\(645\) | −3.52786 | −0.138910 | ||||||||
\(646\) | −20.5623 | −0.809013 | ||||||||
\(647\) | −30.3607 | −1.19360 | −0.596801 | − | 0.802389i | \(-0.703562\pi\) | ||||
−0.596801 | + | 0.802389i | \(0.703562\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.88854 | 0.152521 | ||||||||
\(651\) | 7.32624 | 0.287138 | ||||||||
\(652\) | 5.41641 | 0.212123 | ||||||||
\(653\) | −25.8885 | −1.01310 | −0.506549 | − | 0.862211i | \(-0.669079\pi\) | ||||
−0.506549 | + | 0.862211i | \(0.669079\pi\) | |||||||
\(654\) | 10.5623 | 0.413019 | ||||||||
\(655\) | −6.54102 | −0.255579 | ||||||||
\(656\) | 10.8541 | 0.423781 | ||||||||
\(657\) | −5.23607 | −0.204278 | ||||||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | −35.0344 | −1.36475 | −0.682374 | − | 0.731003i | \(-0.739052\pi\) | ||||
−0.682374 | + | 0.731003i | \(0.739052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.29180 | 0.322513 | 0.161257 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161257 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(662\) | −30.3607 | −1.18000 | ||||||||
\(663\) | 9.70820 | 0.377035 | ||||||||
\(664\) | 8.83282 | 0.342780 | ||||||||
\(665\) | −7.47214 | −0.289757 | ||||||||
\(666\) | 12.0902 | 0.468485 | ||||||||
\(667\) | 6.18034 | 0.239304 | ||||||||
\(668\) | −8.18034 | −0.316507 | ||||||||
\(669\) | −20.7984 | −0.804112 | ||||||||
\(670\) | 22.8328 | 0.882109 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.00000 | 0.192879 | ||||||||
\(673\) | 35.8885 | 1.38340 | 0.691701 | − | 0.722184i | \(-0.256862\pi\) | ||||
0.691701 | + | 0.722184i | \(0.256862\pi\) | |||||||
\(674\) | 27.1459 | 1.04562 | ||||||||
\(675\) | −3.14590 | −0.121086 | ||||||||
\(676\) | 11.4721 | 0.441236 | ||||||||
\(677\) | 23.8885 | 0.918111 | 0.459056 | − | 0.888408i | \(-0.348188\pi\) | ||||
0.459056 | + | 0.888408i | \(0.348188\pi\) | |||||||
\(678\) | 0.763932 | 0.0293386 | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | −67.2492 | −2.57889 | ||||||||
\(681\) | −21.4164 | −0.820679 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.9230 | 1.56587 | 0.782937 | − | 0.622101i | \(-0.213721\pi\) | ||||
0.782937 | + | 0.622101i | \(0.213721\pi\) | |||||||
\(684\) | −2.61803 | −0.100103 | ||||||||
\(685\) | −19.3050 | −0.737604 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −21.2361 | −0.810207 | ||||||||
\(688\) | 1.23607 | 0.0471246 | ||||||||
\(689\) | −15.0557 | −0.573578 | ||||||||
\(690\) | 8.81966 | 0.335759 | ||||||||
\(691\) | 39.9230 | 1.51874 | 0.759371 | − | 0.650658i | \(-0.225507\pi\) | ||||
0.759371 | + | 0.650658i | \(0.225507\pi\) | |||||||
\(692\) | −19.8541 | −0.754740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.3820 | 0.470013 | ||||||||
\(695\) | −13.6950 | −0.519483 | ||||||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | −85.2492 | −3.22904 | ||||||||
\(698\) | −22.7639 | −0.861628 | ||||||||
\(699\) | 5.70820 | 0.215904 | ||||||||
\(700\) | −3.14590 | −0.118904 | ||||||||
\(701\) | 24.0689 | 0.909069 | 0.454535 | − | 0.890729i | \(-0.349806\pi\) | ||||
0.454535 | + | 0.890729i | \(0.349806\pi\) | |||||||
\(702\) | −1.23607 | −0.0466524 | ||||||||
\(703\) | −31.6525 | −1.19380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.70820 | 0.214983 | ||||||||
\(706\) | −12.4721 | −0.469395 | ||||||||
\(707\) | −2.09017 | −0.0786089 | ||||||||
\(708\) | 6.76393 | 0.254204 | ||||||||
\(709\) | −19.6869 | −0.739358 | −0.369679 | − | 0.929160i | \(-0.620532\pi\) | ||||
−0.369679 | + | 0.929160i | \(0.620532\pi\) | |||||||
\(710\) | 25.5279 | 0.958044 | ||||||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | 3.27051 | 0.122568 | ||||||||
\(713\) | 22.6393 | 0.847849 | ||||||||
\(714\) | 7.85410 | 0.293932 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.38197 | −0.313249 | ||||||||
\(717\) | 1.56231 | 0.0583454 | ||||||||
\(718\) | −7.03444 | −0.262523 | ||||||||
\(719\) | 4.87539 | 0.181821 | 0.0909106 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909106 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(720\) | 2.85410 | 0.106366 | ||||||||
\(721\) | −10.3262 | −0.384569 | ||||||||
\(722\) | 12.1459 | 0.452024 | ||||||||
\(723\) | −4.94427 | −0.183879 | ||||||||
\(724\) | 18.9443 | 0.704058 | ||||||||
\(725\) | −6.29180 | −0.233671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7426 | 0.954742 | 0.477371 | − | 0.878702i | \(-0.341590\pi\) | ||||
0.477371 | + | 0.878702i | \(0.341590\pi\) | |||||||
\(728\) | −3.70820 | −0.137435 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.9443 | −0.553112 | ||||||||
\(731\) | −9.70820 | −0.359071 | ||||||||
\(732\) | 8.94427 | 0.330590 | ||||||||
\(733\) | 31.1246 | 1.14961 | 0.574807 | − | 0.818289i | \(-0.305077\pi\) | ||||
0.574807 | + | 0.818289i | \(0.305077\pi\) | |||||||
\(734\) | −16.2705 | −0.600555 | ||||||||
\(735\) | 2.85410 | 0.105275 | ||||||||
\(736\) | 15.4508 | 0.569526 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.8541 | 0.399545 | ||||||||
\(739\) | 49.0132 | 1.80298 | 0.901489 | − | 0.432802i | \(-0.142475\pi\) | ||||
0.901489 | + | 0.432802i | \(0.142475\pi\) | |||||||
\(740\) | −34.5066 | −1.26849 | ||||||||
\(741\) | 3.23607 | 0.118880 | ||||||||
\(742\) | −12.1803 | −0.447154 | ||||||||
\(743\) | 17.3262 | 0.635638 | 0.317819 | − | 0.948151i | \(-0.397050\pi\) | ||||
0.317819 | + | 0.948151i | \(0.397050\pi\) | |||||||
\(744\) | 21.9787 | 0.805779 | ||||||||
\(745\) | 57.0820 | 2.09132 | ||||||||
\(746\) | 23.3262 | 0.854034 | ||||||||
\(747\) | 2.94427 | 0.107725 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.90983 | 0.179401 | ||||||||
\(750\) | 5.29180 | 0.193229 | ||||||||
\(751\) | −10.4721 | −0.382134 | −0.191067 | − | 0.981577i | \(-0.561195\pi\) | ||||
−0.191067 | + | 0.981577i | \(0.561195\pi\) | |||||||
\(752\) | −2.00000 | −0.0729325 | ||||||||
\(753\) | −24.1803 | −0.881181 | ||||||||
\(754\) | −2.47214 | −0.0900299 | ||||||||
\(755\) | 5.70820 | 0.207743 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 0.326238 | 0.0118573 | 0.00592866 | − | 0.999982i | \(-0.498113\pi\) | ||||
0.00592866 | + | 0.999982i | \(0.498113\pi\) | |||||||
\(758\) | −2.47214 | −0.0897920 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.4164 | −0.813129 | ||||||||
\(761\) | 45.7771 | 1.65942 | 0.829709 | − | 0.558196i | \(-0.188506\pi\) | ||||
0.829709 | + | 0.558196i | \(0.188506\pi\) | |||||||
\(762\) | −3.23607 | −0.117230 | ||||||||
\(763\) | 10.5623 | 0.382381 | ||||||||
\(764\) | 18.2705 | 0.661004 | ||||||||
\(765\) | −22.4164 | −0.810467 | ||||||||
\(766\) | 13.0557 | 0.471723 | ||||||||
\(767\) | −8.36068 | −0.301887 | ||||||||
\(768\) | 17.0000 | 0.613435 | ||||||||
\(769\) | 14.5836 | 0.525898 | 0.262949 | − | 0.964810i | \(-0.415305\pi\) | ||||
0.262949 | + | 0.964810i | \(0.415305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.61803 | −0.0942862 | ||||||||
\(772\) | −18.3820 | −0.661581 | ||||||||
\(773\) | −38.9443 | −1.40073 | −0.700364 | − | 0.713786i | \(-0.746979\pi\) | ||||
−0.700364 | + | 0.713786i | \(0.746979\pi\) | |||||||
\(774\) | 1.23607 | 0.0444295 | ||||||||
\(775\) | −23.0476 | −0.827894 | ||||||||
\(776\) | −10.5836 | −0.379929 | ||||||||
\(777\) | 12.0902 | 0.433732 | ||||||||
\(778\) | −22.1803 | −0.795204 | ||||||||
\(779\) | −28.4164 | −1.01812 | ||||||||
\(780\) | 3.52786 | 0.126318 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.2705 | 0.867912 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −27.7082 | −0.988948 | ||||||||
\(786\) | 2.29180 | 0.0817457 | ||||||||
\(787\) | 12.2705 | 0.437396 | 0.218698 | − | 0.975793i | \(-0.429819\pi\) | ||||
0.218698 | + | 0.975793i | \(0.429819\pi\) | |||||||
\(788\) | −4.00000 | −0.142494 | ||||||||
\(789\) | −2.43769 | −0.0867842 | ||||||||
\(790\) | −39.9574 | −1.42162 | ||||||||
\(791\) | 0.763932 | 0.0271623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0557 | −0.392600 | ||||||||
\(794\) | −14.6525 | −0.519997 | ||||||||
\(795\) | 34.7639 | 1.23295 | ||||||||
\(796\) | 2.61803 | 0.0927938 | ||||||||
\(797\) | 10.2705 | 0.363800 | 0.181900 | − | 0.983317i | \(-0.441775\pi\) | ||||
0.181900 | + | 0.983317i | \(0.441775\pi\) | |||||||
\(798\) | 2.61803 | 0.0926774 | ||||||||
\(799\) | 15.7082 | 0.555716 | ||||||||
\(800\) | −15.7295 | −0.556121 | ||||||||
\(801\) | 1.09017 | 0.0385193 | ||||||||
\(802\) | −18.4721 | −0.652274 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 8.81966 | 0.310852 | ||||||||
\(806\) | −9.05573 | −0.318974 | ||||||||
\(807\) | −27.8885 | −0.981723 | ||||||||
\(808\) | −6.27051 | −0.220596 | ||||||||
\(809\) | −28.6525 | −1.00737 | −0.503684 | − | 0.863888i | \(-0.668022\pi\) | ||||
−0.503684 | + | 0.863888i | \(0.668022\pi\) | |||||||
\(810\) | 2.85410 | 0.100283 | ||||||||
\(811\) | −16.3607 | −0.574501 | −0.287251 | − | 0.957855i | \(-0.592741\pi\) | ||||
−0.287251 | + | 0.957855i | \(0.592741\pi\) | |||||||
\(812\) | 2.00000 | 0.0701862 | ||||||||
\(813\) | −24.0902 | −0.844879 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.4590 | 0.541504 | ||||||||
\(816\) | 7.85410 | 0.274949 | ||||||||
\(817\) | −3.23607 | −0.113216 | ||||||||
\(818\) | −28.7639 | −1.00571 | ||||||||
\(819\) | −1.23607 | −0.0431917 | ||||||||
\(820\) | −30.9787 | −1.08182 | ||||||||
\(821\) | 30.3607 | 1.05960 | 0.529798 | − | 0.848124i | \(-0.322268\pi\) | ||||
0.529798 | + | 0.848124i | \(0.322268\pi\) | |||||||
\(822\) | 6.76393 | 0.235919 | ||||||||
\(823\) | 24.4721 | 0.853045 | 0.426523 | − | 0.904477i | \(-0.359738\pi\) | ||||
0.426523 | + | 0.904477i | \(0.359738\pi\) | |||||||
\(824\) | −30.9787 | −1.07919 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.76393 | −0.235347 | ||||||||
\(827\) | −4.32624 | −0.150438 | −0.0752190 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752190 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(828\) | 3.09017 | 0.107391 | ||||||||
\(829\) | 28.9443 | 1.00528 | 0.502638 | − | 0.864497i | \(-0.332363\pi\) | ||||
0.502638 | + | 0.864497i | \(0.332363\pi\) | |||||||
\(830\) | 8.40325 | 0.291681 | ||||||||
\(831\) | 10.4377 | 0.362080 | ||||||||
\(832\) | −8.65248 | −0.299971 | ||||||||
\(833\) | 7.85410 | 0.272129 | ||||||||
\(834\) | 4.79837 | 0.166154 | ||||||||
\(835\) | −23.3475 | −0.807974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.32624 | 0.253232 | ||||||||
\(838\) | −14.7639 | −0.510012 | ||||||||
\(839\) | 33.4164 | 1.15366 | 0.576831 | − | 0.816863i | \(-0.304289\pi\) | ||||
0.576831 | + | 0.816863i | \(0.304289\pi\) | |||||||
\(840\) | 8.56231 | 0.295428 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 4.32624 | 0.149092 | ||||||||
\(843\) | −1.05573 | −0.0363612 | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 32.7426 | 1.12638 | ||||||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.1803 | −0.418275 | ||||||||
\(849\) | −13.4377 | −0.461180 | ||||||||
\(850\) | −24.7082 | −0.847484 | ||||||||
\(851\) | 37.3607 | 1.28071 | ||||||||
\(852\) | 8.94427 | 0.306426 | ||||||||
\(853\) | −15.7082 | −0.537839 | −0.268919 | − | 0.963163i | \(-0.586667\pi\) | ||||
−0.268919 | + | 0.963163i | \(0.586667\pi\) | |||||||
\(854\) | −8.94427 | −0.306067 | ||||||||
\(855\) | −7.47214 | −0.255542 | ||||||||
\(856\) | 14.7295 | 0.503444 | ||||||||
\(857\) | −18.9443 | −0.647124 | −0.323562 | − | 0.946207i | \(-0.604880\pi\) | ||||
−0.323562 | + | 0.946207i | \(0.604880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.88854 | −0.200915 | −0.100457 | − | 0.994941i | \(-0.532031\pi\) | ||||
−0.100457 | + | 0.994941i | \(0.532031\pi\) | |||||||
\(860\) | −3.52786 | −0.120299 | ||||||||
\(861\) | 10.8541 | 0.369907 | ||||||||
\(862\) | 2.09017 | 0.0711915 | ||||||||
\(863\) | 37.6869 | 1.28288 | 0.641439 | − | 0.767174i | \(-0.278338\pi\) | ||||
0.641439 | + | 0.767174i | \(0.278338\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | −56.6656 | −1.92669 | ||||||||
\(866\) | 17.2361 | 0.585705 | ||||||||
\(867\) | −44.6869 | −1.51765 | ||||||||
\(868\) | 7.32624 | 0.248669 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.70820 | 0.193526 | ||||||||
\(871\) | −9.88854 | −0.335061 | ||||||||
\(872\) | 31.6869 | 1.07305 | ||||||||
\(873\) | −3.52786 | −0.119400 | ||||||||
\(874\) | 8.09017 | 0.273654 | ||||||||
\(875\) | 5.29180 | 0.178895 | ||||||||
\(876\) | −5.23607 | −0.176910 | ||||||||
\(877\) | −46.3607 | −1.56549 | −0.782744 | − | 0.622343i | \(-0.786181\pi\) | ||||
−0.782744 | + | 0.622343i | \(0.786181\pi\) | |||||||
\(878\) | 21.7984 | 0.735659 | ||||||||
\(879\) | −19.7984 | −0.667783 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.4508 | −1.12699 | −0.563494 | − | 0.826120i | \(-0.690543\pi\) | ||||
−0.563494 | + | 0.826120i | \(0.690543\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 7.70820 | 0.259402 | 0.129701 | − | 0.991553i | \(-0.458598\pi\) | ||||
0.129701 | + | 0.991553i | \(0.458598\pi\) | |||||||
\(884\) | 9.70820 | 0.326522 | ||||||||
\(885\) | 19.3050 | 0.648929 | ||||||||
\(886\) | −4.90983 | −0.164949 | ||||||||
\(887\) | −46.5410 | −1.56269 | −0.781347 | − | 0.624097i | \(-0.785467\pi\) | ||||
−0.781347 | + | 0.624097i | \(0.785467\pi\) | |||||||
\(888\) | 36.2705 | 1.21716 | ||||||||
\(889\) | −3.23607 | −0.108534 | ||||||||
\(890\) | 3.11146 | 0.104296 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.7984 | −0.696381 | ||||||||
\(893\) | 5.23607 | 0.175218 | ||||||||
\(894\) | −20.0000 | −0.668900 | ||||||||
\(895\) | −23.9230 | −0.799657 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | −3.81966 | −0.127535 | ||||||||
\(898\) | −41.8885 | −1.39784 | ||||||||
\(899\) | 14.6525 | 0.488687 | ||||||||
\(900\) | −3.14590 | −0.104863 | ||||||||
\(901\) | 95.6656 | 3.18708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.23607 | 0.0411338 | ||||||||
\(904\) | 2.29180 | 0.0762240 | ||||||||
\(905\) | 54.0689 | 1.79731 | ||||||||
\(906\) | −2.00000 | −0.0664455 | ||||||||
\(907\) | −47.2361 | −1.56845 | −0.784224 | − | 0.620478i | \(-0.786939\pi\) | ||||
−0.784224 | + | 0.620478i | \(0.786939\pi\) | |||||||
\(908\) | −21.4164 | −0.710728 | ||||||||
\(909\) | −2.09017 | −0.0693266 | ||||||||
\(910\) | −3.52786 | −0.116948 | ||||||||
\(911\) | −11.0557 | −0.366293 | −0.183146 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183146 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(912\) | 2.61803 | 0.0866918 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −12.4721 | −0.412542 | ||||||||
\(915\) | 25.5279 | 0.843925 | ||||||||
\(916\) | −21.2361 | −0.701659 | ||||||||
\(917\) | 2.29180 | 0.0756818 | ||||||||
\(918\) | 7.85410 | 0.259224 | ||||||||
\(919\) | 7.41641 | 0.244645 | 0.122322 | − | 0.992490i | \(-0.460966\pi\) | ||||
0.122322 | + | 0.992490i | \(0.460966\pi\) | |||||||
\(920\) | 26.4590 | 0.872327 | ||||||||
\(921\) | 24.2705 | 0.799740 | ||||||||
\(922\) | 6.36068 | 0.209478 | ||||||||
\(923\) | −11.0557 | −0.363904 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.0344 | −1.25056 | ||||||||
\(926\) | −11.4164 | −0.375166 | ||||||||
\(927\) | −10.3262 | −0.339158 | ||||||||
\(928\) | 10.0000 | 0.328266 | ||||||||
\(929\) | −28.7984 | −0.944844 | −0.472422 | − | 0.881372i | \(-0.656620\pi\) | ||||
−0.472422 | + | 0.881372i | \(0.656620\pi\) | |||||||
\(930\) | 20.9098 | 0.685660 | ||||||||
\(931\) | 2.61803 | 0.0858026 | ||||||||
\(932\) | 5.70820 | 0.186978 | ||||||||
\(933\) | 0.763932 | 0.0250100 | ||||||||
\(934\) | −19.2361 | −0.629423 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.70820 | −0.121206 | ||||||||
\(937\) | 11.7082 | 0.382490 | 0.191245 | − | 0.981542i | \(-0.438747\pi\) | ||||
0.191245 | + | 0.981542i | \(0.438747\pi\) | |||||||
\(938\) | −8.00000 | −0.261209 | ||||||||
\(939\) | 9.81966 | 0.320452 | ||||||||
\(940\) | 5.70820 | 0.186181 | ||||||||
\(941\) | −11.8541 | −0.386433 | −0.193216 | − | 0.981156i | \(-0.561892\pi\) | ||||
−0.193216 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(942\) | 9.70820 | 0.316310 | ||||||||
\(943\) | 33.5410 | 1.09225 | ||||||||
\(944\) | −6.76393 | −0.220147 | ||||||||
\(945\) | 2.85410 | 0.0928439 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4377 | −0.761623 | −0.380811 | − | 0.924653i | \(-0.624355\pi\) | ||||
−0.380811 | + | 0.924653i | \(0.624355\pi\) | |||||||
\(948\) | −14.0000 | −0.454699 | ||||||||
\(949\) | 6.47214 | 0.210094 | ||||||||
\(950\) | −8.23607 | −0.267213 | ||||||||
\(951\) | 27.5967 | 0.894886 | ||||||||
\(952\) | 23.5623 | 0.763659 | ||||||||
\(953\) | 4.83282 | 0.156550 | 0.0782751 | − | 0.996932i | \(-0.475059\pi\) | ||||
0.0782751 | + | 0.996932i | \(0.475059\pi\) | |||||||
\(954\) | −12.1803 | −0.394353 | ||||||||
\(955\) | 52.1459 | 1.68740 | ||||||||
\(956\) | 1.56231 | 0.0505286 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.0557 | 0.357194 | ||||||||
\(959\) | 6.76393 | 0.218419 | ||||||||
\(960\) | 19.9787 | 0.644810 | ||||||||
\(961\) | 22.6738 | 0.731412 | ||||||||
\(962\) | −14.9443 | −0.481823 | ||||||||
\(963\) | 4.90983 | 0.158217 | ||||||||
\(964\) | −4.94427 | −0.159244 | ||||||||
\(965\) | −52.4640 | −1.68888 | ||||||||
\(966\) | −3.09017 | −0.0994246 | ||||||||
\(967\) | 49.3050 | 1.58554 | 0.792770 | − | 0.609521i | \(-0.208638\pi\) | ||||
0.792770 | + | 0.609521i | \(0.208638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.5623 | −0.660556 | ||||||||
\(970\) | −10.0689 | −0.323292 | ||||||||
\(971\) | 42.0689 | 1.35005 | 0.675027 | − | 0.737793i | \(-0.264132\pi\) | ||||
0.675027 | + | 0.737793i | \(0.264132\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 4.79837 | 0.153829 | ||||||||
\(974\) | 39.2361 | 1.25720 | ||||||||
\(975\) | 3.88854 | 0.124533 | ||||||||
\(976\) | −8.94427 | −0.286299 | ||||||||
\(977\) | −26.5836 | −0.850484 | −0.425242 | − | 0.905080i | \(-0.639811\pi\) | ||||
−0.425242 | + | 0.905080i | \(0.639811\pi\) | |||||||
\(978\) | −5.41641 | −0.173198 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.85410 | 0.0911709 | ||||||||
\(981\) | 10.5623 | 0.337228 | ||||||||
\(982\) | 0.326238 | 0.0104107 | ||||||||
\(983\) | 48.4721 | 1.54602 | 0.773011 | − | 0.634393i | \(-0.218750\pi\) | ||||
0.773011 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(984\) | 32.5623 | 1.03805 | ||||||||
\(985\) | −11.4164 | −0.363757 | ||||||||
\(986\) | 15.7082 | 0.500251 | ||||||||
\(987\) | −2.00000 | −0.0636607 | ||||||||
\(988\) | 3.23607 | 0.102953 | ||||||||
\(989\) | 3.81966 | 0.121458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6525 | 0.592515 | 0.296258 | − | 0.955108i | \(-0.404261\pi\) | ||||
0.296258 | + | 0.955108i | \(0.404261\pi\) | |||||||
\(992\) | 36.6312 | 1.16304 | ||||||||
\(993\) | −30.3607 | −0.963467 | ||||||||
\(994\) | −8.94427 | −0.283695 | ||||||||
\(995\) | 7.47214 | 0.236883 | ||||||||
\(996\) | 2.94427 | 0.0932928 | ||||||||
\(997\) | −52.5410 | −1.66399 | −0.831995 | − | 0.554783i | \(-0.812801\pi\) | ||||
−0.831995 | + | 0.554783i | \(0.812801\pi\) | |||||||
\(998\) | −26.1803 | −0.828724 | ||||||||
\(999\) | 12.0902 | 0.382516 |
(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 | 2541.2.a.n.1.1 | 2 | ||
3.2 | odd | 2 | 7623.2.a.bu.1.2 | 2 | |||
11.5 | even | 5 | 231.2.j.c.190.1 | yes | 4 | ||
11.9 | even | 5 | 231.2.j.c.169.1 | ✓ | 4 | ||
11.10 | odd | 2 | 2541.2.a.bd.1.1 | 2 | |||
33.5 | odd | 10 | 693.2.m.c.190.1 | 4 | |||
33.20 | odd | 10 | 693.2.m.c.631.1 | 4 | |||
33.32 | even | 2 | 7623.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.c.169.1 | ✓ | 4 | 11.9 | even | 5 | ||
231.2.j.c.190.1 | yes | 4 | 11.5 | even | 5 | ||
693.2.m.c.190.1 | 4 | 33.5 | odd | 10 | |||
693.2.m.c.631.1 | 4 | 33.20 | odd | 10 | |||
2541.2.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2541.2.a.bd.1.1 | 2 | 11.10 | odd | 2 | |||
7623.2.a.w.1.2 | 2 | 33.32 | even | 2 | |||
7623.2.a.bu.1.2 | 2 | 3.2 | odd | 2 |