Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-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 | ||||||||
\(7\) | −3.61803 | −1.36749 | −0.683744 | − | 0.729722i | \(-0.739650\pi\) | ||||
−0.683744 | + | 0.729722i | \(0.739650\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.85410 | 0.514235 | 0.257118 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257118 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(14\) | −3.61803 | −0.966960 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.47214 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.85410 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.61803 | 0.789520 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.38197 | −1.33073 | −0.665366 | − | 0.746517i | \(-0.731724\pi\) | ||||
−0.665366 | + | 0.746517i | \(0.731724\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.85410 | 0.363619 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.61803 | −0.683744 | ||||||||
\(29\) | 2.76393 | 0.513249 | 0.256625 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256625 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.47214 | −0.423968 | ||||||||
\(35\) | −3.61803 | −0.611559 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.85410 | −1.62000 | −0.810002 | − | 0.586427i | \(-0.800534\pi\) | ||||
−0.810002 | + | 0.586427i | \(0.800534\pi\) | |||||||
\(38\) | 1.85410 | 0.300775 | ||||||||
\(39\) | −1.85410 | −0.296894 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 10.0902 | 1.57582 | 0.787910 | − | 0.615791i | \(-0.211163\pi\) | ||||
0.787910 | + | 0.615791i | \(0.211163\pi\) | |||||||
\(42\) | 3.61803 | 0.558275 | ||||||||
\(43\) | −3.23607 | −0.493496 | −0.246748 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246748 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −6.38197 | −0.940970 | ||||||||
\(47\) | −12.7984 | −1.86683 | −0.933417 | − | 0.358792i | \(-0.883189\pi\) | ||||
−0.933417 | + | 0.358792i | \(0.883189\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 6.09017 | 0.870024 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 1.85410 | 0.257118 | ||||||||
\(53\) | −1.90983 | −0.262335 | −0.131168 | − | 0.991360i | \(-0.541873\pi\) | ||||
−0.131168 | + | 0.991360i | \(0.541873\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.61803 | −0.483480 | ||||||||
\(57\) | −1.85410 | −0.245582 | ||||||||
\(58\) | 2.76393 | 0.362922 | ||||||||
\(59\) | 6.32624 | 0.823606 | 0.411803 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411803 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 9.70820 | 1.24301 | 0.621504 | − | 0.783411i | \(-0.286522\pi\) | ||||
0.621504 | + | 0.783411i | \(0.286522\pi\) | |||||||
\(62\) | −2.76393 | −0.351020 | ||||||||
\(63\) | −3.61803 | −0.455829 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.85410 | 0.229973 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.29180 | −0.279987 | −0.139994 | − | 0.990152i | \(-0.544708\pi\) | ||||
−0.139994 | + | 0.990152i | \(0.544708\pi\) | |||||||
\(68\) | −2.47214 | −0.299791 | ||||||||
\(69\) | 6.38197 | 0.768298 | ||||||||
\(70\) | −3.61803 | −0.432438 | ||||||||
\(71\) | −14.1803 | −1.68290 | −0.841448 | − | 0.540338i | \(-0.818297\pi\) | ||||
−0.841448 | + | 0.540338i | \(0.818297\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −9.85410 | −1.14552 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 1.85410 | 0.212680 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.85410 | −0.209936 | ||||||||
\(79\) | −12.4721 | −1.40322 | −0.701612 | − | 0.712559i | \(-0.747536\pi\) | ||||
−0.701612 | + | 0.712559i | \(0.747536\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0902 | 1.11427 | ||||||||
\(83\) | 2.47214 | 0.271352 | 0.135676 | − | 0.990753i | \(-0.456679\pi\) | ||||
0.135676 | + | 0.990753i | \(0.456679\pi\) | |||||||
\(84\) | 3.61803 | 0.394760 | ||||||||
\(85\) | −2.47214 | −0.268141 | ||||||||
\(86\) | −3.23607 | −0.348954 | ||||||||
\(87\) | −2.76393 | −0.296325 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.56231 | −0.907603 | −0.453801 | − | 0.891103i | \(-0.649932\pi\) | ||||
−0.453801 | + | 0.891103i | \(0.649932\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −6.70820 | −0.703211 | ||||||||
\(92\) | −6.38197 | −0.665366 | ||||||||
\(93\) | 2.76393 | 0.286606 | ||||||||
\(94\) | −12.7984 | −1.32005 | ||||||||
\(95\) | 1.85410 | 0.190227 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 6.09017 | 0.615200 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −19.4164 | −1.93200 | −0.966002 | − | 0.258533i | \(-0.916761\pi\) | ||||
−0.966002 | + | 0.258533i | \(0.916761\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | 1.85410 | 0.182690 | 0.0913450 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913450 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(104\) | 1.85410 | 0.181810 | ||||||||
\(105\) | 3.61803 | 0.353084 | ||||||||
\(106\) | −1.90983 | −0.185499 | ||||||||
\(107\) | 10.4721 | 1.01238 | 0.506190 | − | 0.862422i | \(-0.331054\pi\) | ||||
0.506190 | + | 0.862422i | \(0.331054\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −19.4164 | −1.85975 | −0.929877 | − | 0.367870i | \(-0.880087\pi\) | ||||
−0.929877 | + | 0.367870i | \(0.880087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.85410 | 0.935310 | ||||||||
\(112\) | −3.61803 | −0.341872 | ||||||||
\(113\) | −12.4721 | −1.17328 | −0.586640 | − | 0.809848i | \(-0.699550\pi\) | ||||
−0.586640 | + | 0.809848i | \(0.699550\pi\) | |||||||
\(114\) | −1.85410 | −0.173653 | ||||||||
\(115\) | −6.38197 | −0.595121 | ||||||||
\(116\) | 2.76393 | 0.256625 | ||||||||
\(117\) | 1.85410 | 0.171412 | ||||||||
\(118\) | 6.32624 | 0.582377 | ||||||||
\(119\) | 8.94427 | 0.819920 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.70820 | 0.878939 | ||||||||
\(123\) | −10.0902 | −0.909800 | ||||||||
\(124\) | −2.76393 | −0.248208 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.61803 | −0.322320 | ||||||||
\(127\) | −9.56231 | −0.848517 | −0.424259 | − | 0.905541i | \(-0.639465\pi\) | ||||
−0.424259 | + | 0.905541i | \(0.639465\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.23607 | 0.284920 | ||||||||
\(130\) | 1.85410 | 0.162615 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.70820 | −0.581675 | ||||||||
\(134\) | −2.29180 | −0.197981 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −2.47214 | −0.211984 | ||||||||
\(137\) | 7.41641 | 0.633626 | 0.316813 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316813 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(138\) | 6.38197 | 0.543269 | ||||||||
\(139\) | 3.79837 | 0.322174 | 0.161087 | − | 0.986940i | \(-0.448500\pi\) | ||||
0.161087 | + | 0.986940i | \(0.448500\pi\) | |||||||
\(140\) | −3.61803 | −0.305780 | ||||||||
\(141\) | 12.7984 | 1.07782 | ||||||||
\(142\) | −14.1803 | −1.18999 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.76393 | 0.229532 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | −6.09017 | −0.502309 | ||||||||
\(148\) | −9.85410 | −0.810002 | ||||||||
\(149\) | 6.47214 | 0.530218 | 0.265109 | − | 0.964218i | \(-0.414592\pi\) | ||||
0.265109 | + | 0.964218i | \(0.414592\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −20.4721 | −1.66600 | −0.832999 | − | 0.553274i | \(-0.813378\pi\) | ||||
−0.832999 | + | 0.553274i | \(0.813378\pi\) | |||||||
\(152\) | 1.85410 | 0.150388 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.76393 | −0.222004 | ||||||||
\(156\) | −1.85410 | −0.148447 | ||||||||
\(157\) | −8.85410 | −0.706634 | −0.353317 | − | 0.935504i | \(-0.614946\pi\) | ||||
−0.353317 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(158\) | −12.4721 | −0.992230 | ||||||||
\(159\) | 1.90983 | 0.151459 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 23.0902 | 1.81976 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 23.4164 | 1.83411 | 0.917057 | − | 0.398755i | \(-0.130558\pi\) | ||||
0.917057 | + | 0.398755i | \(0.130558\pi\) | |||||||
\(164\) | 10.0902 | 0.787910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.47214 | 0.191875 | ||||||||
\(167\) | 6.03444 | 0.466959 | 0.233480 | − | 0.972362i | \(-0.424989\pi\) | ||||
0.233480 | + | 0.972362i | \(0.424989\pi\) | |||||||
\(168\) | 3.61803 | 0.279137 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | −2.47214 | −0.189604 | ||||||||
\(171\) | 1.85410 | 0.141787 | ||||||||
\(172\) | −3.23607 | −0.246748 | ||||||||
\(173\) | −12.3820 | −0.941383 | −0.470692 | − | 0.882298i | \(-0.655996\pi\) | ||||
−0.470692 | + | 0.882298i | \(0.655996\pi\) | |||||||
\(174\) | −2.76393 | −0.209533 | ||||||||
\(175\) | −3.61803 | −0.273498 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.32624 | −0.475509 | ||||||||
\(178\) | −8.56231 | −0.641772 | ||||||||
\(179\) | −0.0901699 | −0.00673962 | −0.00336981 | − | 0.999994i | \(-0.501073\pi\) | ||||
−0.00336981 | + | 0.999994i | \(0.501073\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −6.70820 | −0.497245 | ||||||||
\(183\) | −9.70820 | −0.717651 | ||||||||
\(184\) | −6.38197 | −0.470485 | ||||||||
\(185\) | −9.85410 | −0.724488 | ||||||||
\(186\) | 2.76393 | 0.202661 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.7984 | −0.933417 | ||||||||
\(189\) | 3.61803 | 0.263173 | ||||||||
\(190\) | 1.85410 | 0.134511 | ||||||||
\(191\) | 16.1803 | 1.17077 | 0.585384 | − | 0.810756i | \(-0.300944\pi\) | ||||
0.585384 | + | 0.810756i | \(0.300944\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.7082 | 0.842775 | 0.421387 | − | 0.906881i | \(-0.361543\pi\) | ||||
0.421387 | + | 0.906881i | \(0.361543\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | −1.85410 | −0.132775 | ||||||||
\(196\) | 6.09017 | 0.435012 | ||||||||
\(197\) | 12.3820 | 0.882179 | 0.441089 | − | 0.897463i | \(-0.354592\pi\) | ||||
0.441089 | + | 0.897463i | \(0.354592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.47214 | −0.458798 | −0.229399 | − | 0.973333i | \(-0.573676\pi\) | ||||
−0.229399 | + | 0.973333i | \(0.573676\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 2.29180 | 0.161651 | ||||||||
\(202\) | −19.4164 | −1.36613 | ||||||||
\(203\) | −10.0000 | −0.701862 | ||||||||
\(204\) | 2.47214 | 0.173084 | ||||||||
\(205\) | 10.0902 | 0.704728 | ||||||||
\(206\) | 1.85410 | 0.129181 | ||||||||
\(207\) | −6.38197 | −0.443577 | ||||||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.61803 | 0.249668 | ||||||||
\(211\) | 5.52786 | 0.380554 | 0.190277 | − | 0.981730i | \(-0.439061\pi\) | ||||
0.190277 | + | 0.981730i | \(0.439061\pi\) | |||||||
\(212\) | −1.90983 | −0.131168 | ||||||||
\(213\) | 14.1803 | 0.971621 | ||||||||
\(214\) | 10.4721 | 0.715860 | ||||||||
\(215\) | −3.23607 | −0.220698 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | −19.4164 | −1.31505 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.58359 | −0.308326 | ||||||||
\(222\) | 9.85410 | 0.661364 | ||||||||
\(223\) | −28.5623 | −1.91267 | −0.956337 | − | 0.292267i | \(-0.905590\pi\) | ||||
−0.956337 | + | 0.292267i | \(0.905590\pi\) | |||||||
\(224\) | −3.61803 | −0.241740 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −12.4721 | −0.829634 | ||||||||
\(227\) | 2.29180 | 0.152112 | 0.0760559 | − | 0.997104i | \(-0.475767\pi\) | ||||
0.0760559 | + | 0.997104i | \(0.475767\pi\) | |||||||
\(228\) | −1.85410 | −0.122791 | ||||||||
\(229\) | 22.9443 | 1.51620 | 0.758100 | − | 0.652138i | \(-0.226128\pi\) | ||||
0.758100 | + | 0.652138i | \(0.226128\pi\) | |||||||
\(230\) | −6.38197 | −0.420814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.76393 | 0.181461 | ||||||||
\(233\) | 1.23607 | 0.0809775 | 0.0404888 | − | 0.999180i | \(-0.487109\pi\) | ||||
0.0404888 | + | 0.999180i | \(0.487109\pi\) | |||||||
\(234\) | 1.85410 | 0.121206 | ||||||||
\(235\) | −12.7984 | −0.834874 | ||||||||
\(236\) | 6.32624 | 0.411803 | ||||||||
\(237\) | 12.4721 | 0.810152 | ||||||||
\(238\) | 8.94427 | 0.579771 | ||||||||
\(239\) | −10.1803 | −0.658511 | −0.329256 | − | 0.944241i | \(-0.606798\pi\) | ||||
−0.329256 | + | 0.944241i | \(0.606798\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −14.5623 | −0.938041 | −0.469020 | − | 0.883187i | \(-0.655393\pi\) | ||||
−0.469020 | + | 0.883187i | \(0.655393\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.70820 | 0.621504 | ||||||||
\(245\) | 6.09017 | 0.389087 | ||||||||
\(246\) | −10.0902 | −0.643326 | ||||||||
\(247\) | 3.43769 | 0.218735 | ||||||||
\(248\) | −2.76393 | −0.175510 | ||||||||
\(249\) | −2.47214 | −0.156665 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −19.3262 | −1.21986 | −0.609931 | − | 0.792455i | \(-0.708803\pi\) | ||||
−0.609931 | + | 0.792455i | \(0.708803\pi\) | |||||||
\(252\) | −3.61803 | −0.227915 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.56231 | −0.599992 | ||||||||
\(255\) | 2.47214 | 0.154811 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.4721 | −1.77604 | −0.888022 | − | 0.459802i | \(-0.847920\pi\) | ||||
−0.888022 | + | 0.459802i | \(0.847920\pi\) | |||||||
\(258\) | 3.23607 | 0.201469 | ||||||||
\(259\) | 35.6525 | 2.21534 | ||||||||
\(260\) | 1.85410 | 0.114987 | ||||||||
\(261\) | 2.76393 | 0.171083 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.61803 | 0.161435 | 0.0807174 | − | 0.996737i | \(-0.474279\pi\) | ||||
0.0807174 | + | 0.996737i | \(0.474279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.90983 | −0.117320 | ||||||||
\(266\) | −6.70820 | −0.411306 | ||||||||
\(267\) | 8.56231 | 0.524005 | ||||||||
\(268\) | −2.29180 | −0.139994 | ||||||||
\(269\) | 27.5967 | 1.68260 | 0.841302 | − | 0.540566i | \(-0.181790\pi\) | ||||
0.841302 | + | 0.540566i | \(0.181790\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −19.7082 | −1.19719 | −0.598594 | − | 0.801053i | \(-0.704274\pi\) | ||||
−0.598594 | + | 0.801053i | \(0.704274\pi\) | |||||||
\(272\) | −2.47214 | −0.149895 | ||||||||
\(273\) | 6.70820 | 0.405999 | ||||||||
\(274\) | 7.41641 | 0.448042 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.38197 | 0.384149 | ||||||||
\(277\) | 30.7426 | 1.84715 | 0.923573 | − | 0.383422i | \(-0.125254\pi\) | ||||
0.923573 | + | 0.383422i | \(0.125254\pi\) | |||||||
\(278\) | 3.79837 | 0.227811 | ||||||||
\(279\) | −2.76393 | −0.165472 | ||||||||
\(280\) | −3.61803 | −0.216219 | ||||||||
\(281\) | 9.05573 | 0.540219 | 0.270110 | − | 0.962830i | \(-0.412940\pi\) | ||||
0.270110 | + | 0.962830i | \(0.412940\pi\) | |||||||
\(282\) | 12.7984 | 0.762132 | ||||||||
\(283\) | 23.1246 | 1.37462 | 0.687308 | − | 0.726366i | \(-0.258792\pi\) | ||||
0.687308 | + | 0.726366i | \(0.258792\pi\) | |||||||
\(284\) | −14.1803 | −0.841448 | ||||||||
\(285\) | −1.85410 | −0.109828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.5066 | −2.15492 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 2.76393 | 0.162304 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | −22.0902 | −1.29052 | −0.645261 | − | 0.763962i | \(-0.723251\pi\) | ||||
−0.645261 | + | 0.763962i | \(0.723251\pi\) | |||||||
\(294\) | −6.09017 | −0.355186 | ||||||||
\(295\) | 6.32624 | 0.368328 | ||||||||
\(296\) | −9.85410 | −0.572758 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.47214 | 0.374921 | ||||||||
\(299\) | −11.8328 | −0.684309 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 11.7082 | 0.674850 | ||||||||
\(302\) | −20.4721 | −1.17804 | ||||||||
\(303\) | 19.4164 | 1.11544 | ||||||||
\(304\) | 1.85410 | 0.106340 | ||||||||
\(305\) | 9.70820 | 0.555890 | ||||||||
\(306\) | −2.47214 | −0.141323 | ||||||||
\(307\) | −26.8328 | −1.53143 | −0.765715 | − | 0.643180i | \(-0.777615\pi\) | ||||
−0.765715 | + | 0.643180i | \(0.777615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.85410 | −0.105476 | ||||||||
\(310\) | −2.76393 | −0.156981 | ||||||||
\(311\) | −23.8885 | −1.35460 | −0.677298 | − | 0.735709i | \(-0.736849\pi\) | ||||
−0.677298 | + | 0.735709i | \(0.736849\pi\) | |||||||
\(312\) | −1.85410 | −0.104968 | ||||||||
\(313\) | 5.70820 | 0.322647 | 0.161323 | − | 0.986902i | \(-0.448424\pi\) | ||||
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(314\) | −8.85410 | −0.499666 | ||||||||
\(315\) | −3.61803 | −0.203853 | ||||||||
\(316\) | −12.4721 | −0.701612 | ||||||||
\(317\) | −10.9098 | −0.612757 | −0.306379 | − | 0.951910i | \(-0.599117\pi\) | ||||
−0.306379 | + | 0.951910i | \(0.599117\pi\) | |||||||
\(318\) | 1.90983 | 0.107098 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −10.4721 | −0.584498 | ||||||||
\(322\) | 23.0902 | 1.28676 | ||||||||
\(323\) | −4.58359 | −0.255038 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.85410 | 0.102847 | ||||||||
\(326\) | 23.4164 | 1.29691 | ||||||||
\(327\) | 19.4164 | 1.07373 | ||||||||
\(328\) | 10.0902 | 0.557136 | ||||||||
\(329\) | 46.3050 | 2.55287 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1459 | 0.557669 | 0.278834 | − | 0.960339i | \(-0.410052\pi\) | ||||
0.278834 | + | 0.960339i | \(0.410052\pi\) | |||||||
\(332\) | 2.47214 | 0.135676 | ||||||||
\(333\) | −9.85410 | −0.540001 | ||||||||
\(334\) | 6.03444 | 0.330190 | ||||||||
\(335\) | −2.29180 | −0.125214 | ||||||||
\(336\) | 3.61803 | 0.197380 | ||||||||
\(337\) | 23.4164 | 1.27557 | 0.637787 | − | 0.770213i | \(-0.279850\pi\) | ||||
0.637787 | + | 0.770213i | \(0.279850\pi\) | |||||||
\(338\) | −9.56231 | −0.520121 | ||||||||
\(339\) | 12.4721 | 0.677393 | ||||||||
\(340\) | −2.47214 | −0.134070 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.85410 | 0.100258 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −3.23607 | −0.174477 | ||||||||
\(345\) | 6.38197 | 0.343594 | ||||||||
\(346\) | −12.3820 | −0.665659 | ||||||||
\(347\) | −9.70820 | −0.521164 | −0.260582 | − | 0.965452i | \(-0.583914\pi\) | ||||
−0.260582 | + | 0.965452i | \(0.583914\pi\) | |||||||
\(348\) | −2.76393 | −0.148162 | ||||||||
\(349\) | 13.4164 | 0.718164 | 0.359082 | − | 0.933306i | \(-0.383090\pi\) | ||||
0.359082 | + | 0.933306i | \(0.383090\pi\) | |||||||
\(350\) | −3.61803 | −0.193392 | ||||||||
\(351\) | −1.85410 | −0.0989646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.23607 | −0.0657893 | −0.0328946 | − | 0.999459i | \(-0.510473\pi\) | ||||
−0.0328946 | + | 0.999459i | \(0.510473\pi\) | |||||||
\(354\) | −6.32624 | −0.336236 | ||||||||
\(355\) | −14.1803 | −0.752614 | ||||||||
\(356\) | −8.56231 | −0.453801 | ||||||||
\(357\) | −8.94427 | −0.473381 | ||||||||
\(358\) | −0.0901699 | −0.00476563 | ||||||||
\(359\) | 29.2361 | 1.54302 | 0.771510 | − | 0.636217i | \(-0.219502\pi\) | ||||
0.771510 | + | 0.636217i | \(0.219502\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −15.5623 | −0.819069 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.70820 | −0.351605 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | −9.70820 | −0.507456 | ||||||||
\(367\) | 35.4164 | 1.84872 | 0.924361 | − | 0.381520i | \(-0.124599\pi\) | ||||
0.924361 | + | 0.381520i | \(0.124599\pi\) | |||||||
\(368\) | −6.38197 | −0.332683 | ||||||||
\(369\) | 10.0902 | 0.525273 | ||||||||
\(370\) | −9.85410 | −0.512290 | ||||||||
\(371\) | 6.90983 | 0.358741 | ||||||||
\(372\) | 2.76393 | 0.143303 | ||||||||
\(373\) | 14.4377 | 0.747555 | 0.373778 | − | 0.927518i | \(-0.378062\pi\) | ||||
0.373778 | + | 0.927518i | \(0.378062\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −12.7984 | −0.660026 | ||||||||
\(377\) | 5.12461 | 0.263931 | ||||||||
\(378\) | 3.61803 | 0.186092 | ||||||||
\(379\) | 33.5066 | 1.72112 | 0.860559 | − | 0.509351i | \(-0.170115\pi\) | ||||
0.860559 | + | 0.509351i | \(0.170115\pi\) | |||||||
\(380\) | 1.85410 | 0.0951134 | ||||||||
\(381\) | 9.56231 | 0.489892 | ||||||||
\(382\) | 16.1803 | 0.827858 | ||||||||
\(383\) | −26.7426 | −1.36649 | −0.683243 | − | 0.730191i | \(-0.739431\pi\) | ||||
−0.683243 | + | 0.730191i | \(0.739431\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.7082 | 0.595932 | ||||||||
\(387\) | −3.23607 | −0.164499 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | −1.85410 | −0.0938861 | ||||||||
\(391\) | 15.7771 | 0.797882 | ||||||||
\(392\) | 6.09017 | 0.307600 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.3820 | 0.623794 | ||||||||
\(395\) | −12.4721 | −0.627541 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.74265 | 0.338404 | 0.169202 | − | 0.985581i | \(-0.445881\pi\) | ||||
0.169202 | + | 0.985581i | \(0.445881\pi\) | |||||||
\(398\) | −6.47214 | −0.324419 | ||||||||
\(399\) | 6.70820 | 0.335830 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.09017 | −0.0544405 | −0.0272202 | − | 0.999629i | \(-0.508666\pi\) | ||||
−0.0272202 | + | 0.999629i | \(0.508666\pi\) | |||||||
\(402\) | 2.29180 | 0.114304 | ||||||||
\(403\) | −5.12461 | −0.255275 | ||||||||
\(404\) | −19.4164 | −0.966002 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | 2.43769 | 0.120536 | 0.0602681 | − | 0.998182i | \(-0.480804\pi\) | ||||
0.0602681 | + | 0.998182i | \(0.480804\pi\) | |||||||
\(410\) | 10.0902 | 0.498318 | ||||||||
\(411\) | −7.41641 | −0.365824 | ||||||||
\(412\) | 1.85410 | 0.0913450 | ||||||||
\(413\) | −22.8885 | −1.12627 | ||||||||
\(414\) | −6.38197 | −0.313657 | ||||||||
\(415\) | 2.47214 | 0.121352 | ||||||||
\(416\) | 1.85410 | 0.0909048 | ||||||||
\(417\) | −3.79837 | −0.186007 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7984 | 1.01607 | 0.508034 | − | 0.861337i | \(-0.330373\pi\) | ||||
0.508034 | + | 0.861337i | \(0.330373\pi\) | |||||||
\(420\) | 3.61803 | 0.176542 | ||||||||
\(421\) | −4.11146 | −0.200380 | −0.100190 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100190 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(422\) | 5.52786 | 0.269092 | ||||||||
\(423\) | −12.7984 | −0.622278 | ||||||||
\(424\) | −1.90983 | −0.0927495 | ||||||||
\(425\) | −2.47214 | −0.119916 | ||||||||
\(426\) | 14.1803 | 0.687040 | ||||||||
\(427\) | −35.1246 | −1.69980 | ||||||||
\(428\) | 10.4721 | 0.506190 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.23607 | −0.156057 | ||||||||
\(431\) | −3.34752 | −0.161245 | −0.0806223 | − | 0.996745i | \(-0.525691\pi\) | ||||
−0.0806223 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −13.1246 | −0.630729 | −0.315364 | − | 0.948971i | \(-0.602127\pi\) | ||||
−0.315364 | + | 0.948971i | \(0.602127\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | −2.76393 | −0.132520 | ||||||||
\(436\) | −19.4164 | −0.929877 | ||||||||
\(437\) | −11.8328 | −0.566040 | ||||||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | 33.7082 | 1.60880 | 0.804402 | − | 0.594085i | \(-0.202486\pi\) | ||||
0.804402 | + | 0.594085i | \(0.202486\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.09017 | 0.290008 | ||||||||
\(442\) | −4.58359 | −0.218019 | ||||||||
\(443\) | −0.472136 | −0.0224319 | −0.0112159 | − | 0.999937i | \(-0.503570\pi\) | ||||
−0.0112159 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(444\) | 9.85410 | 0.467655 | ||||||||
\(445\) | −8.56231 | −0.405892 | ||||||||
\(446\) | −28.5623 | −1.35246 | ||||||||
\(447\) | −6.47214 | −0.306122 | ||||||||
\(448\) | −3.61803 | −0.170936 | ||||||||
\(449\) | 26.9098 | 1.26995 | 0.634977 | − | 0.772531i | \(-0.281010\pi\) | ||||
0.634977 | + | 0.772531i | \(0.281010\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.4721 | −0.586640 | ||||||||
\(453\) | 20.4721 | 0.961865 | ||||||||
\(454\) | 2.29180 | 0.107559 | ||||||||
\(455\) | −6.70820 | −0.314485 | ||||||||
\(456\) | −1.85410 | −0.0868263 | ||||||||
\(457\) | −18.8328 | −0.880962 | −0.440481 | − | 0.897762i | \(-0.645192\pi\) | ||||
−0.440481 | + | 0.897762i | \(0.645192\pi\) | |||||||
\(458\) | 22.9443 | 1.07212 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | −6.38197 | −0.297561 | ||||||||
\(461\) | −2.29180 | −0.106740 | −0.0533698 | − | 0.998575i | \(-0.516996\pi\) | ||||
−0.0533698 | + | 0.998575i | \(0.516996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2705 | 1.36032 | 0.680158 | − | 0.733066i | \(-0.261911\pi\) | ||||
0.680158 | + | 0.733066i | \(0.261911\pi\) | |||||||
\(464\) | 2.76393 | 0.128312 | ||||||||
\(465\) | 2.76393 | 0.128174 | ||||||||
\(466\) | 1.23607 | 0.0572597 | ||||||||
\(467\) | −18.4721 | −0.854789 | −0.427394 | − | 0.904065i | \(-0.640568\pi\) | ||||
−0.427394 | + | 0.904065i | \(0.640568\pi\) | |||||||
\(468\) | 1.85410 | 0.0857059 | ||||||||
\(469\) | 8.29180 | 0.382880 | ||||||||
\(470\) | −12.7984 | −0.590345 | ||||||||
\(471\) | 8.85410 | 0.407975 | ||||||||
\(472\) | 6.32624 | 0.291189 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.4721 | 0.572864 | ||||||||
\(475\) | 1.85410 | 0.0850720 | ||||||||
\(476\) | 8.94427 | 0.409960 | ||||||||
\(477\) | −1.90983 | −0.0874451 | ||||||||
\(478\) | −10.1803 | −0.465638 | ||||||||
\(479\) | −7.23607 | −0.330624 | −0.165312 | − | 0.986241i | \(-0.552863\pi\) | ||||
−0.165312 | + | 0.986241i | \(0.552863\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −18.2705 | −0.833064 | ||||||||
\(482\) | −14.5623 | −0.663295 | ||||||||
\(483\) | −23.0902 | −1.05064 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 3.41641 | 0.154812 | 0.0774061 | − | 0.997000i | \(-0.475336\pi\) | ||||
0.0774061 | + | 0.997000i | \(0.475336\pi\) | |||||||
\(488\) | 9.70820 | 0.439470 | ||||||||
\(489\) | −23.4164 | −1.05893 | ||||||||
\(490\) | 6.09017 | 0.275126 | ||||||||
\(491\) | −26.3262 | −1.18809 | −0.594043 | − | 0.804433i | \(-0.702469\pi\) | ||||
−0.594043 | + | 0.804433i | \(0.702469\pi\) | |||||||
\(492\) | −10.0902 | −0.454900 | ||||||||
\(493\) | −6.83282 | −0.307735 | ||||||||
\(494\) | 3.43769 | 0.154669 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.76393 | −0.124104 | ||||||||
\(497\) | 51.3050 | 2.30134 | ||||||||
\(498\) | −2.47214 | −0.110779 | ||||||||
\(499\) | 32.5623 | 1.45769 | 0.728845 | − | 0.684679i | \(-0.240058\pi\) | ||||
0.728845 | + | 0.684679i | \(0.240058\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −6.03444 | −0.269599 | ||||||||
\(502\) | −19.3262 | −0.862572 | ||||||||
\(503\) | −41.4508 | −1.84820 | −0.924101 | − | 0.382148i | \(-0.875184\pi\) | ||||
−0.924101 | + | 0.382148i | \(0.875184\pi\) | |||||||
\(504\) | −3.61803 | −0.161160 | ||||||||
\(505\) | −19.4164 | −0.864019 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.56231 | 0.424677 | ||||||||
\(508\) | −9.56231 | −0.424259 | ||||||||
\(509\) | −18.3607 | −0.813823 | −0.406911 | − | 0.913468i | \(-0.633394\pi\) | ||||
−0.406911 | + | 0.913468i | \(0.633394\pi\) | |||||||
\(510\) | 2.47214 | 0.109468 | ||||||||
\(511\) | −7.23607 | −0.320105 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.85410 | −0.0818606 | ||||||||
\(514\) | −28.4721 | −1.25585 | ||||||||
\(515\) | 1.85410 | 0.0817015 | ||||||||
\(516\) | 3.23607 | 0.142460 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 35.6525 | 1.56648 | ||||||||
\(519\) | 12.3820 | 0.543508 | ||||||||
\(520\) | 1.85410 | 0.0813077 | ||||||||
\(521\) | 11.7984 | 0.516896 | 0.258448 | − | 0.966025i | \(-0.416789\pi\) | ||||
0.258448 | + | 0.966025i | \(0.416789\pi\) | |||||||
\(522\) | 2.76393 | 0.120974 | ||||||||
\(523\) | 19.5967 | 0.856906 | 0.428453 | − | 0.903564i | \(-0.359059\pi\) | ||||
0.428453 | + | 0.903564i | \(0.359059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.61803 | 0.157904 | ||||||||
\(526\) | 2.61803 | 0.114152 | ||||||||
\(527\) | 6.83282 | 0.297642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.7295 | 0.770847 | ||||||||
\(530\) | −1.90983 | −0.0829577 | ||||||||
\(531\) | 6.32624 | 0.274535 | ||||||||
\(532\) | −6.70820 | −0.290838 | ||||||||
\(533\) | 18.7082 | 0.810342 | ||||||||
\(534\) | 8.56231 | 0.370527 | ||||||||
\(535\) | 10.4721 | 0.452750 | ||||||||
\(536\) | −2.29180 | −0.0989905 | ||||||||
\(537\) | 0.0901699 | 0.00389112 | ||||||||
\(538\) | 27.5967 | 1.18978 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 11.4164 | 0.490830 | 0.245415 | − | 0.969418i | \(-0.421076\pi\) | ||||
0.245415 | + | 0.969418i | \(0.421076\pi\) | |||||||
\(542\) | −19.7082 | −0.846540 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.47214 | −0.105992 | ||||||||
\(545\) | −19.4164 | −0.831708 | ||||||||
\(546\) | 6.70820 | 0.287085 | ||||||||
\(547\) | 14.2918 | 0.611073 | 0.305537 | − | 0.952180i | \(-0.401164\pi\) | ||||
0.305537 | + | 0.952180i | \(0.401164\pi\) | |||||||
\(548\) | 7.41641 | 0.316813 | ||||||||
\(549\) | 9.70820 | 0.414336 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12461 | 0.218316 | ||||||||
\(552\) | 6.38197 | 0.271635 | ||||||||
\(553\) | 45.1246 | 1.91889 | ||||||||
\(554\) | 30.7426 | 1.30613 | ||||||||
\(555\) | 9.85410 | 0.418283 | ||||||||
\(556\) | 3.79837 | 0.161087 | ||||||||
\(557\) | 3.49342 | 0.148021 | 0.0740105 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740105 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(558\) | −2.76393 | −0.117007 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | −3.61803 | −0.152890 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.05573 | 0.381993 | ||||||||
\(563\) | −26.4721 | −1.11567 | −0.557834 | − | 0.829953i | \(-0.688367\pi\) | ||||
−0.557834 | + | 0.829953i | \(0.688367\pi\) | |||||||
\(564\) | 12.7984 | 0.538909 | ||||||||
\(565\) | −12.4721 | −0.524707 | ||||||||
\(566\) | 23.1246 | 0.972000 | ||||||||
\(567\) | −3.61803 | −0.151943 | ||||||||
\(568\) | −14.1803 | −0.594994 | ||||||||
\(569\) | 13.3262 | 0.558665 | 0.279332 | − | 0.960194i | \(-0.409887\pi\) | ||||
0.279332 | + | 0.960194i | \(0.409887\pi\) | |||||||
\(570\) | −1.85410 | −0.0776598 | ||||||||
\(571\) | −27.9787 | −1.17087 | −0.585436 | − | 0.810718i | \(-0.699077\pi\) | ||||
−0.585436 | + | 0.810718i | \(0.699077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.1803 | −0.675943 | ||||||||
\(574\) | −36.5066 | −1.52376 | ||||||||
\(575\) | −6.38197 | −0.266146 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.29180 | −0.178670 | −0.0893349 | − | 0.996002i | \(-0.528474\pi\) | ||||
−0.0893349 | + | 0.996002i | \(0.528474\pi\) | |||||||
\(578\) | −10.8885 | −0.452904 | ||||||||
\(579\) | −11.7082 | −0.486576 | ||||||||
\(580\) | 2.76393 | 0.114766 | ||||||||
\(581\) | −8.94427 | −0.371071 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 1.85410 | 0.0766577 | ||||||||
\(586\) | −22.0902 | −0.912537 | ||||||||
\(587\) | −20.9443 | −0.864463 | −0.432231 | − | 0.901763i | \(-0.642274\pi\) | ||||
−0.432231 | + | 0.901763i | \(0.642274\pi\) | |||||||
\(588\) | −6.09017 | −0.251154 | ||||||||
\(589\) | −5.12461 | −0.211156 | ||||||||
\(590\) | 6.32624 | 0.260447 | ||||||||
\(591\) | −12.3820 | −0.509326 | ||||||||
\(592\) | −9.85410 | −0.405001 | ||||||||
\(593\) | 11.8885 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.94427 | 0.366679 | ||||||||
\(596\) | 6.47214 | 0.265109 | ||||||||
\(597\) | 6.47214 | 0.264887 | ||||||||
\(598\) | −11.8328 | −0.483880 | ||||||||
\(599\) | −22.1803 | −0.906264 | −0.453132 | − | 0.891443i | \(-0.649693\pi\) | ||||
−0.453132 | + | 0.891443i | \(0.649693\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 6.79837 | 0.277311 | 0.138656 | − | 0.990341i | \(-0.455722\pi\) | ||||
0.138656 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(602\) | 11.7082 | 0.477191 | ||||||||
\(603\) | −2.29180 | −0.0933292 | ||||||||
\(604\) | −20.4721 | −0.832999 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19.4164 | 0.788738 | ||||||||
\(607\) | 3.41641 | 0.138668 | 0.0693339 | − | 0.997594i | \(-0.477913\pi\) | ||||
0.0693339 | + | 0.997594i | \(0.477913\pi\) | |||||||
\(608\) | 1.85410 | 0.0751938 | ||||||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | 9.70820 | 0.393074 | ||||||||
\(611\) | −23.7295 | −0.959992 | ||||||||
\(612\) | −2.47214 | −0.0999302 | ||||||||
\(613\) | 41.4164 | 1.67279 | 0.836396 | − | 0.548125i | \(-0.184658\pi\) | ||||
0.836396 | + | 0.548125i | \(0.184658\pi\) | |||||||
\(614\) | −26.8328 | −1.08288 | ||||||||
\(615\) | −10.0902 | −0.406875 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0000 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(618\) | −1.85410 | −0.0745829 | ||||||||
\(619\) | 6.43769 | 0.258753 | 0.129376 | − | 0.991596i | \(-0.458702\pi\) | ||||
0.129376 | + | 0.991596i | \(0.458702\pi\) | |||||||
\(620\) | −2.76393 | −0.111002 | ||||||||
\(621\) | 6.38197 | 0.256099 | ||||||||
\(622\) | −23.8885 | −0.957843 | ||||||||
\(623\) | 30.9787 | 1.24114 | ||||||||
\(624\) | −1.85410 | −0.0742235 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.70820 | 0.228146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.85410 | −0.353317 | ||||||||
\(629\) | 24.3607 | 0.971324 | ||||||||
\(630\) | −3.61803 | −0.144146 | ||||||||
\(631\) | 8.76393 | 0.348887 | 0.174443 | − | 0.984667i | \(-0.444187\pi\) | ||||
0.174443 | + | 0.984667i | \(0.444187\pi\) | |||||||
\(632\) | −12.4721 | −0.496115 | ||||||||
\(633\) | −5.52786 | −0.219713 | ||||||||
\(634\) | −10.9098 | −0.433285 | ||||||||
\(635\) | −9.56231 | −0.379469 | ||||||||
\(636\) | 1.90983 | 0.0757297 | ||||||||
\(637\) | 11.2918 | 0.447397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1803 | −0.560966 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −31.6312 | −1.24936 | −0.624678 | − | 0.780882i | \(-0.714770\pi\) | ||||
−0.624678 | + | 0.780882i | \(0.714770\pi\) | |||||||
\(642\) | −10.4721 | −0.413302 | ||||||||
\(643\) | 40.0000 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 23.0902 | 0.909880 | ||||||||
\(645\) | 3.23607 | 0.127420 | ||||||||
\(646\) | −4.58359 | −0.180339 | ||||||||
\(647\) | −49.8885 | −1.96132 | −0.980661 | − | 0.195716i | \(-0.937297\pi\) | ||||
−0.980661 | + | 0.195716i | \(0.937297\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.85410 | 0.0727239 | ||||||||
\(651\) | −10.0000 | −0.391931 | ||||||||
\(652\) | 23.4164 | 0.917057 | ||||||||
\(653\) | 46.6869 | 1.82700 | 0.913500 | − | 0.406838i | \(-0.133369\pi\) | ||||
0.913500 | + | 0.406838i | \(0.133369\pi\) | |||||||
\(654\) | 19.4164 | 0.759242 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.0902 | 0.393955 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 46.3050 | 1.80515 | ||||||||
\(659\) | −8.67376 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6525 | −0.414333 | −0.207167 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207167 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(662\) | 10.1459 | 0.394332 | ||||||||
\(663\) | 4.58359 | 0.178012 | ||||||||
\(664\) | 2.47214 | 0.0959375 | ||||||||
\(665\) | −6.70820 | −0.260133 | ||||||||
\(666\) | −9.85410 | −0.381839 | ||||||||
\(667\) | −17.6393 | −0.682997 | ||||||||
\(668\) | 6.03444 | 0.233480 | ||||||||
\(669\) | 28.5623 | 1.10428 | ||||||||
\(670\) | −2.29180 | −0.0885398 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | 25.2361 | 0.972779 | 0.486389 | − | 0.873742i | \(-0.338314\pi\) | ||||
0.486389 | + | 0.873742i | \(0.338314\pi\) | |||||||
\(674\) | 23.4164 | 0.901966 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −9.56231 | −0.367781 | ||||||||
\(677\) | 34.3607 | 1.32059 | 0.660294 | − | 0.751007i | \(-0.270432\pi\) | ||||
0.660294 | + | 0.751007i | \(0.270432\pi\) | |||||||
\(678\) | 12.4721 | 0.478989 | ||||||||
\(679\) | 7.23607 | 0.277695 | ||||||||
\(680\) | −2.47214 | −0.0948021 | ||||||||
\(681\) | −2.29180 | −0.0878218 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0132 | −1.26321 | −0.631607 | − | 0.775289i | \(-0.717604\pi\) | ||||
−0.631607 | + | 0.775289i | \(0.717604\pi\) | |||||||
\(684\) | 1.85410 | 0.0708934 | ||||||||
\(685\) | 7.41641 | 0.283366 | ||||||||
\(686\) | 3.29180 | 0.125681 | ||||||||
\(687\) | −22.9443 | −0.875379 | ||||||||
\(688\) | −3.23607 | −0.123374 | ||||||||
\(689\) | −3.54102 | −0.134902 | ||||||||
\(690\) | 6.38197 | 0.242957 | ||||||||
\(691\) | 35.7984 | 1.36183 | 0.680917 | − | 0.732360i | \(-0.261581\pi\) | ||||
0.680917 | + | 0.732360i | \(0.261581\pi\) | |||||||
\(692\) | −12.3820 | −0.470692 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.70820 | −0.368518 | ||||||||
\(695\) | 3.79837 | 0.144081 | ||||||||
\(696\) | −2.76393 | −0.104767 | ||||||||
\(697\) | −24.9443 | −0.944832 | ||||||||
\(698\) | 13.4164 | 0.507819 | ||||||||
\(699\) | −1.23607 | −0.0467524 | ||||||||
\(700\) | −3.61803 | −0.136749 | ||||||||
\(701\) | 48.0689 | 1.81554 | 0.907768 | − | 0.419472i | \(-0.137785\pi\) | ||||
0.907768 | + | 0.419472i | \(0.137785\pi\) | |||||||
\(702\) | −1.85410 | −0.0699786 | ||||||||
\(703\) | −18.2705 | −0.689085 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.7984 | 0.482015 | ||||||||
\(706\) | −1.23607 | −0.0465200 | ||||||||
\(707\) | 70.2492 | 2.64199 | ||||||||
\(708\) | −6.32624 | −0.237755 | ||||||||
\(709\) | 10.7639 | 0.404248 | 0.202124 | − | 0.979360i | \(-0.435216\pi\) | ||||
0.202124 | + | 0.979360i | \(0.435216\pi\) | |||||||
\(710\) | −14.1803 | −0.532179 | ||||||||
\(711\) | −12.4721 | −0.467742 | ||||||||
\(712\) | −8.56231 | −0.320886 | ||||||||
\(713\) | 17.6393 | 0.660598 | ||||||||
\(714\) | −8.94427 | −0.334731 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0901699 | −0.00336981 | ||||||||
\(717\) | 10.1803 | 0.380192 | ||||||||
\(718\) | 29.2361 | 1.09108 | ||||||||
\(719\) | 23.5279 | 0.877441 | 0.438721 | − | 0.898624i | \(-0.355432\pi\) | ||||
0.438721 | + | 0.898624i | \(0.355432\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −6.70820 | −0.249827 | ||||||||
\(722\) | −15.5623 | −0.579169 | ||||||||
\(723\) | 14.5623 | 0.541578 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.76393 | 0.102650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.6869 | 1.84279 | 0.921393 | − | 0.388632i | \(-0.127052\pi\) | ||||
0.921393 | + | 0.388632i | \(0.127052\pi\) | |||||||
\(728\) | −6.70820 | −0.248623 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | −9.70820 | −0.358826 | ||||||||
\(733\) | −37.4164 | −1.38201 | −0.691003 | − | 0.722852i | \(-0.742831\pi\) | ||||
−0.691003 | + | 0.722852i | \(0.742831\pi\) | |||||||
\(734\) | 35.4164 | 1.30724 | ||||||||
\(735\) | −6.09017 | −0.224639 | ||||||||
\(736\) | −6.38197 | −0.235242 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.0902 | 0.371424 | ||||||||
\(739\) | −10.8541 | −0.399275 | −0.199637 | − | 0.979870i | \(-0.563976\pi\) | ||||
−0.199637 | + | 0.979870i | \(0.563976\pi\) | |||||||
\(740\) | −9.85410 | −0.362244 | ||||||||
\(741\) | −3.43769 | −0.126287 | ||||||||
\(742\) | 6.90983 | 0.253668 | ||||||||
\(743\) | −10.3820 | −0.380877 | −0.190439 | − | 0.981699i | \(-0.560991\pi\) | ||||
−0.190439 | + | 0.981699i | \(0.560991\pi\) | |||||||
\(744\) | 2.76393 | 0.101331 | ||||||||
\(745\) | 6.47214 | 0.237121 | ||||||||
\(746\) | 14.4377 | 0.528602 | ||||||||
\(747\) | 2.47214 | 0.0904507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.8885 | −1.38442 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 35.4164 | 1.29236 | 0.646182 | − | 0.763184i | \(-0.276365\pi\) | ||||
0.646182 | + | 0.763184i | \(0.276365\pi\) | |||||||
\(752\) | −12.7984 | −0.466709 | ||||||||
\(753\) | 19.3262 | 0.704287 | ||||||||
\(754\) | 5.12461 | 0.186627 | ||||||||
\(755\) | −20.4721 | −0.745057 | ||||||||
\(756\) | 3.61803 | 0.131587 | ||||||||
\(757\) | −19.1591 | −0.696348 | −0.348174 | − | 0.937430i | \(-0.613198\pi\) | ||||
−0.348174 | + | 0.937430i | \(0.613198\pi\) | |||||||
\(758\) | 33.5066 | 1.21701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.85410 | 0.0672553 | ||||||||
\(761\) | 0.111456 | 0.00404028 | 0.00202014 | − | 0.999998i | \(-0.499357\pi\) | ||||
0.00202014 | + | 0.999998i | \(0.499357\pi\) | |||||||
\(762\) | 9.56231 | 0.346406 | ||||||||
\(763\) | 70.2492 | 2.54319 | ||||||||
\(764\) | 16.1803 | 0.585384 | ||||||||
\(765\) | −2.47214 | −0.0893803 | ||||||||
\(766\) | −26.7426 | −0.966251 | ||||||||
\(767\) | 11.7295 | 0.423527 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 47.0902 | 1.69811 | 0.849057 | − | 0.528300i | \(-0.177171\pi\) | ||||
0.849057 | + | 0.528300i | \(0.177171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.4721 | 1.02540 | ||||||||
\(772\) | 11.7082 | 0.421387 | ||||||||
\(773\) | 22.0902 | 0.794528 | 0.397264 | − | 0.917704i | \(-0.369960\pi\) | ||||
0.397264 | + | 0.917704i | \(0.369960\pi\) | |||||||
\(774\) | −3.23607 | −0.116318 | ||||||||
\(775\) | −2.76393 | −0.0992834 | ||||||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | −35.6525 | −1.27903 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | 18.7082 | 0.670291 | ||||||||
\(780\) | −1.85410 | −0.0663875 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.7771 | 0.564188 | ||||||||
\(783\) | −2.76393 | −0.0987749 | ||||||||
\(784\) | 6.09017 | 0.217506 | ||||||||
\(785\) | −8.85410 | −0.316016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7082 | 0.702522 | 0.351261 | − | 0.936278i | \(-0.385753\pi\) | ||||
0.351261 | + | 0.936278i | \(0.385753\pi\) | |||||||
\(788\) | 12.3820 | 0.441089 | ||||||||
\(789\) | −2.61803 | −0.0932045 | ||||||||
\(790\) | −12.4721 | −0.443739 | ||||||||
\(791\) | 45.1246 | 1.60445 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 6.74265 | 0.239288 | ||||||||
\(795\) | 1.90983 | 0.0677347 | ||||||||
\(796\) | −6.47214 | −0.229399 | ||||||||
\(797\) | 33.0902 | 1.17211 | 0.586057 | − | 0.810270i | \(-0.300679\pi\) | ||||
0.586057 | + | 0.810270i | \(0.300679\pi\) | |||||||
\(798\) | 6.70820 | 0.237468 | ||||||||
\(799\) | 31.6393 | 1.11932 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −8.56231 | −0.302534 | ||||||||
\(802\) | −1.09017 | −0.0384952 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.29180 | 0.0808254 | ||||||||
\(805\) | 23.0902 | 0.813822 | ||||||||
\(806\) | −5.12461 | −0.180507 | ||||||||
\(807\) | −27.5967 | −0.971452 | ||||||||
\(808\) | −19.4164 | −0.683067 | ||||||||
\(809\) | −25.7426 | −0.905063 | −0.452532 | − | 0.891748i | \(-0.649479\pi\) | ||||
−0.452532 | + | 0.891748i | \(0.649479\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −28.9230 | −1.01562 | −0.507812 | − | 0.861468i | \(-0.669545\pi\) | ||||
−0.507812 | + | 0.861468i | \(0.669545\pi\) | |||||||
\(812\) | −10.0000 | −0.350931 | ||||||||
\(813\) | 19.7082 | 0.691197 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.4164 | 0.820241 | ||||||||
\(816\) | 2.47214 | 0.0865421 | ||||||||
\(817\) | −6.00000 | −0.209913 | ||||||||
\(818\) | 2.43769 | 0.0852320 | ||||||||
\(819\) | −6.70820 | −0.234404 | ||||||||
\(820\) | 10.0902 | 0.352364 | ||||||||
\(821\) | −31.0132 | −1.08237 | −0.541183 | − | 0.840905i | \(-0.682023\pi\) | ||||
−0.541183 | + | 0.840905i | \(0.682023\pi\) | |||||||
\(822\) | −7.41641 | −0.258677 | ||||||||
\(823\) | −13.8541 | −0.482924 | −0.241462 | − | 0.970410i | \(-0.577627\pi\) | ||||
−0.241462 | + | 0.970410i | \(0.577627\pi\) | |||||||
\(824\) | 1.85410 | 0.0645907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.8885 | −0.796394 | ||||||||
\(827\) | 34.6525 | 1.20498 | 0.602492 | − | 0.798125i | \(-0.294174\pi\) | ||||
0.602492 | + | 0.798125i | \(0.294174\pi\) | |||||||
\(828\) | −6.38197 | −0.221789 | ||||||||
\(829\) | −13.0557 | −0.453444 | −0.226722 | − | 0.973959i | \(-0.572801\pi\) | ||||
−0.226722 | + | 0.973959i | \(0.572801\pi\) | |||||||
\(830\) | 2.47214 | 0.0858091 | ||||||||
\(831\) | −30.7426 | −1.06645 | ||||||||
\(832\) | 1.85410 | 0.0642794 | ||||||||
\(833\) | −15.0557 | −0.521650 | ||||||||
\(834\) | −3.79837 | −0.131527 | ||||||||
\(835\) | 6.03444 | 0.208830 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.76393 | 0.0955355 | ||||||||
\(838\) | 20.7984 | 0.718468 | ||||||||
\(839\) | 41.4853 | 1.43223 | 0.716116 | − | 0.697982i | \(-0.245918\pi\) | ||||
0.716116 | + | 0.697982i | \(0.245918\pi\) | |||||||
\(840\) | 3.61803 | 0.124834 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | −4.11146 | −0.141690 | ||||||||
\(843\) | −9.05573 | −0.311896 | ||||||||
\(844\) | 5.52786 | 0.190277 | ||||||||
\(845\) | −9.56231 | −0.328953 | ||||||||
\(846\) | −12.7984 | −0.440017 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.90983 | −0.0655838 | ||||||||
\(849\) | −23.1246 | −0.793635 | ||||||||
\(850\) | −2.47214 | −0.0847936 | ||||||||
\(851\) | 62.8885 | 2.15579 | ||||||||
\(852\) | 14.1803 | 0.485810 | ||||||||
\(853\) | −33.6180 | −1.15106 | −0.575530 | − | 0.817781i | \(-0.695204\pi\) | ||||
−0.575530 | + | 0.817781i | \(0.695204\pi\) | |||||||
\(854\) | −35.1246 | −1.20194 | ||||||||
\(855\) | 1.85410 | 0.0634089 | ||||||||
\(856\) | 10.4721 | 0.357930 | ||||||||
\(857\) | −11.5967 | −0.396137 | −0.198069 | − | 0.980188i | \(-0.563467\pi\) | ||||
−0.198069 | + | 0.980188i | \(0.563467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5066 | 0.870273 | 0.435137 | − | 0.900364i | \(-0.356700\pi\) | ||||
0.435137 | + | 0.900364i | \(0.356700\pi\) | |||||||
\(860\) | −3.23607 | −0.110349 | ||||||||
\(861\) | 36.5066 | 1.24414 | ||||||||
\(862\) | −3.34752 | −0.114017 | ||||||||
\(863\) | 38.3951 | 1.30699 | 0.653493 | − | 0.756933i | \(-0.273303\pi\) | ||||
0.653493 | + | 0.756933i | \(0.273303\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −12.3820 | −0.420999 | ||||||||
\(866\) | −13.1246 | −0.445992 | ||||||||
\(867\) | 10.8885 | 0.369794 | ||||||||
\(868\) | 10.0000 | 0.339422 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.76393 | −0.0937061 | ||||||||
\(871\) | −4.24922 | −0.143979 | ||||||||
\(872\) | −19.4164 | −0.657523 | ||||||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | −11.8328 | −0.400251 | ||||||||
\(875\) | −3.61803 | −0.122312 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 17.8541 | 0.602890 | 0.301445 | − | 0.953484i | \(-0.402531\pi\) | ||||
0.301445 | + | 0.953484i | \(0.402531\pi\) | |||||||
\(878\) | 33.7082 | 1.13760 | ||||||||
\(879\) | 22.0902 | 0.745083 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.5066 | −0.994102 | −0.497051 | − | 0.867721i | \(-0.665584\pi\) | ||||
−0.497051 | + | 0.867721i | \(0.665584\pi\) | |||||||
\(882\) | 6.09017 | 0.205067 | ||||||||
\(883\) | −11.4164 | −0.384193 | −0.192096 | − | 0.981376i | \(-0.561529\pi\) | ||||
−0.192096 | + | 0.981376i | \(0.561529\pi\) | |||||||
\(884\) | −4.58359 | −0.154163 | ||||||||
\(885\) | −6.32624 | −0.212654 | ||||||||
\(886\) | −0.472136 | −0.0158617 | ||||||||
\(887\) | −17.6180 | −0.591556 | −0.295778 | − | 0.955257i | \(-0.595579\pi\) | ||||
−0.295778 | + | 0.955257i | \(0.595579\pi\) | |||||||
\(888\) | 9.85410 | 0.330682 | ||||||||
\(889\) | 34.5967 | 1.16034 | ||||||||
\(890\) | −8.56231 | −0.287009 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.5623 | −0.956337 | ||||||||
\(893\) | −23.7295 | −0.794077 | ||||||||
\(894\) | −6.47214 | −0.216461 | ||||||||
\(895\) | −0.0901699 | −0.00301405 | ||||||||
\(896\) | −3.61803 | −0.120870 | ||||||||
\(897\) | 11.8328 | 0.395086 | ||||||||
\(898\) | 26.9098 | 0.897993 | ||||||||
\(899\) | −7.63932 | −0.254786 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 4.72136 | 0.157291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.7082 | −0.389625 | ||||||||
\(904\) | −12.4721 | −0.414817 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.4721 | 0.680141 | ||||||||
\(907\) | −22.2492 | −0.738773 | −0.369387 | − | 0.929276i | \(-0.620432\pi\) | ||||
−0.369387 | + | 0.929276i | \(0.620432\pi\) | |||||||
\(908\) | 2.29180 | 0.0760559 | ||||||||
\(909\) | −19.4164 | −0.644002 | ||||||||
\(910\) | −6.70820 | −0.222375 | ||||||||
\(911\) | 35.0132 | 1.16004 | 0.580019 | − | 0.814603i | \(-0.303045\pi\) | ||||
0.580019 | + | 0.814603i | \(0.303045\pi\) | |||||||
\(912\) | −1.85410 | −0.0613955 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −18.8328 | −0.622934 | ||||||||
\(915\) | −9.70820 | −0.320943 | ||||||||
\(916\) | 22.9443 | 0.758100 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.47214 | 0.0815926 | ||||||||
\(919\) | −22.6525 | −0.747236 | −0.373618 | − | 0.927583i | \(-0.621883\pi\) | ||||
−0.373618 | + | 0.927583i | \(0.621883\pi\) | |||||||
\(920\) | −6.38197 | −0.210407 | ||||||||
\(921\) | 26.8328 | 0.884171 | ||||||||
\(922\) | −2.29180 | −0.0754763 | ||||||||
\(923\) | −26.2918 | −0.865405 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.85410 | −0.324001 | ||||||||
\(926\) | 29.2705 | 0.961889 | ||||||||
\(927\) | 1.85410 | 0.0608967 | ||||||||
\(928\) | 2.76393 | 0.0907305 | ||||||||
\(929\) | −32.5623 | −1.06833 | −0.534167 | − | 0.845379i | \(-0.679375\pi\) | ||||
−0.534167 | + | 0.845379i | \(0.679375\pi\) | |||||||
\(930\) | 2.76393 | 0.0906329 | ||||||||
\(931\) | 11.2918 | 0.370074 | ||||||||
\(932\) | 1.23607 | 0.0404888 | ||||||||
\(933\) | 23.8885 | 0.782076 | ||||||||
\(934\) | −18.4721 | −0.604427 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.85410 | 0.0606032 | ||||||||
\(937\) | 38.8328 | 1.26861 | 0.634306 | − | 0.773082i | \(-0.281286\pi\) | ||||
0.634306 | + | 0.773082i | \(0.281286\pi\) | |||||||
\(938\) | 8.29180 | 0.270737 | ||||||||
\(939\) | −5.70820 | −0.186280 | ||||||||
\(940\) | −12.7984 | −0.417437 | ||||||||
\(941\) | 35.7771 | 1.16630 | 0.583150 | − | 0.812365i | \(-0.301820\pi\) | ||||
0.583150 | + | 0.812365i | \(0.301820\pi\) | |||||||
\(942\) | 8.85410 | 0.288482 | ||||||||
\(943\) | −64.3951 | −2.09699 | ||||||||
\(944\) | 6.32624 | 0.205902 | ||||||||
\(945\) | 3.61803 | 0.117695 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.05573 | −0.294272 | −0.147136 | − | 0.989116i | \(-0.547005\pi\) | ||||
−0.147136 | + | 0.989116i | \(0.547005\pi\) | |||||||
\(948\) | 12.4721 | 0.405076 | ||||||||
\(949\) | 3.70820 | 0.120373 | ||||||||
\(950\) | 1.85410 | 0.0601550 | ||||||||
\(951\) | 10.9098 | 0.353775 | ||||||||
\(952\) | 8.94427 | 0.289886 | ||||||||
\(953\) | −39.0132 | −1.26376 | −0.631880 | − | 0.775066i | \(-0.717716\pi\) | ||||
−0.631880 | + | 0.775066i | \(0.717716\pi\) | |||||||
\(954\) | −1.90983 | −0.0618330 | ||||||||
\(955\) | 16.1803 | 0.523584 | ||||||||
\(956\) | −10.1803 | −0.329256 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.23607 | −0.233787 | ||||||||
\(959\) | −26.8328 | −0.866477 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | −18.2705 | −0.589065 | ||||||||
\(963\) | 10.4721 | 0.337460 | ||||||||
\(964\) | −14.5623 | −0.469020 | ||||||||
\(965\) | 11.7082 | 0.376900 | ||||||||
\(966\) | −23.0902 | −0.742914 | ||||||||
\(967\) | −11.0213 | −0.354421 | −0.177210 | − | 0.984173i | \(-0.556707\pi\) | ||||
−0.177210 | + | 0.984173i | \(0.556707\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.58359 | 0.147246 | ||||||||
\(970\) | −2.00000 | −0.0642161 | ||||||||
\(971\) | −25.0344 | −0.803393 | −0.401697 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401697 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −13.7426 | −0.440569 | ||||||||
\(974\) | 3.41641 | 0.109469 | ||||||||
\(975\) | −1.85410 | −0.0593788 | ||||||||
\(976\) | 9.70820 | 0.310752 | ||||||||
\(977\) | 18.9443 | 0.606081 | 0.303040 | − | 0.952978i | \(-0.401998\pi\) | ||||
0.303040 | + | 0.952978i | \(0.401998\pi\) | |||||||
\(978\) | −23.4164 | −0.748774 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.09017 | 0.194543 | ||||||||
\(981\) | −19.4164 | −0.619918 | ||||||||
\(982\) | −26.3262 | −0.840104 | ||||||||
\(983\) | −12.2705 | −0.391368 | −0.195684 | − | 0.980667i | \(-0.562693\pi\) | ||||
−0.195684 | + | 0.980667i | \(0.562693\pi\) | |||||||
\(984\) | −10.0902 | −0.321663 | ||||||||
\(985\) | 12.3820 | 0.394522 | ||||||||
\(986\) | −6.83282 | −0.217601 | ||||||||
\(987\) | −46.3050 | −1.47390 | ||||||||
\(988\) | 3.43769 | 0.109368 | ||||||||
\(989\) | 20.6525 | 0.656711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | −2.76393 | −0.0877549 | ||||||||
\(993\) | −10.1459 | −0.321970 | ||||||||
\(994\) | 51.3050 | 1.62729 | ||||||||
\(995\) | −6.47214 | −0.205181 | ||||||||
\(996\) | −2.47214 | −0.0783326 | ||||||||
\(997\) | −22.0000 | −0.696747 | −0.348373 | − | 0.937356i | \(-0.613266\pi\) | ||||
−0.348373 | + | 0.937356i | \(0.613266\pi\) | |||||||
\(998\) | 32.5623 | 1.03074 | ||||||||
\(999\) | 9.85410 | 0.311770 |
(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 | 3630.2.a.bl.1.1 | 2 | ||
11.3 | even | 5 | 330.2.m.a.31.1 | ✓ | 4 | ||
11.4 | even | 5 | 330.2.m.a.181.1 | yes | 4 | ||
11.10 | odd | 2 | 3630.2.a.bf.1.2 | 2 | |||
33.14 | odd | 10 | 990.2.n.h.361.1 | 4 | |||
33.26 | odd | 10 | 990.2.n.h.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.a.31.1 | ✓ | 4 | 11.3 | even | 5 | ||
330.2.m.a.181.1 | yes | 4 | 11.4 | even | 5 | ||
990.2.n.h.181.1 | 4 | 33.26 | odd | 10 | |||
990.2.n.h.361.1 | 4 | 33.14 | odd | 10 | |||
3630.2.a.bf.1.2 | 2 | 11.10 | odd | 2 | |||
3630.2.a.bl.1.1 | 2 | 1.1 | even | 1 | trivial |