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: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) 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 | ||||||||
\(7\) | −3.73205 | −1.41058 | −0.705291 | − | 0.708918i | \(-0.749184\pi\) | ||||
−0.705291 | + | 0.708918i | \(0.749184\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 3.73205 | 0.997433 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.267949 | −0.0649872 | −0.0324936 | − | 0.999472i | \(-0.510345\pi\) | ||||
−0.0324936 | + | 0.999472i | \(0.510345\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.46410 | 1.02414 | 0.512068 | − | 0.858945i | \(-0.328880\pi\) | ||||
0.512068 | + | 0.858945i | \(0.328880\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.73205 | −0.814400 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.73205 | −0.986701 | −0.493350 | − | 0.869831i | \(-0.664228\pi\) | ||||
−0.493350 | + | 0.869831i | \(0.664228\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.73205 | −0.705291 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 8.19615 | 1.47207 | 0.736036 | − | 0.676942i | \(-0.236695\pi\) | ||||
0.736036 | + | 0.676942i | \(0.236695\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.267949 | 0.0459529 | ||||||||
\(35\) | −3.73205 | −0.630832 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.73205 | −0.284747 | −0.142374 | − | 0.989813i | \(-0.545473\pi\) | ||||
−0.142374 | + | 0.989813i | \(0.545473\pi\) | |||||||
\(38\) | −4.46410 | −0.724173 | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.73205 | −0.739022 | −0.369511 | − | 0.929226i | \(-0.620475\pi\) | ||||
−0.369511 | + | 0.929226i | \(0.620475\pi\) | |||||||
\(42\) | 3.73205 | 0.575868 | ||||||||
\(43\) | −6.73205 | −1.02663 | −0.513314 | − | 0.858201i | \(-0.671582\pi\) | ||||
−0.513314 | + | 0.858201i | \(0.671582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 4.73205 | 0.697703 | ||||||||
\(47\) | 8.92820 | 1.30231 | 0.651156 | − | 0.758944i | \(-0.274284\pi\) | ||||
0.651156 | + | 0.758944i | \(0.274284\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.267949 | −0.0375204 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | −5.26795 | −0.723608 | −0.361804 | − | 0.932254i | \(-0.617839\pi\) | ||||
−0.361804 | + | 0.932254i | \(0.617839\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.73205 | 0.498716 | ||||||||
\(57\) | 4.46410 | 0.591285 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | −4.19615 | −0.546293 | −0.273146 | − | 0.961973i | \(-0.588064\pi\) | ||||
−0.273146 | + | 0.961973i | \(0.588064\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 2.19615 | 0.281189 | 0.140594 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140594 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(62\) | −8.19615 | −1.04091 | ||||||||
\(63\) | −3.73205 | −0.470194 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4641 | −1.40056 | −0.700281 | − | 0.713867i | \(-0.746942\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(68\) | −0.267949 | −0.0324936 | ||||||||
\(69\) | −4.73205 | −0.569672 | ||||||||
\(70\) | 3.73205 | 0.446065 | ||||||||
\(71\) | −9.92820 | −1.17826 | −0.589130 | − | 0.808038i | \(-0.700530\pi\) | ||||
−0.589130 | + | 0.808038i | \(0.700530\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.19615 | −0.725205 | −0.362602 | − | 0.931944i | \(-0.618112\pi\) | ||||
−0.362602 | + | 0.931944i | \(0.618112\pi\) | |||||||
\(74\) | 1.73205 | 0.201347 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.46410 | 0.512068 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | −0.535898 | −0.0602933 | −0.0301466 | − | 0.999545i | \(-0.509597\pi\) | ||||
−0.0301466 | + | 0.999545i | \(0.509597\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.73205 | 0.522568 | ||||||||
\(83\) | 11.3923 | 1.25047 | 0.625234 | − | 0.780437i | \(-0.285004\pi\) | ||||
0.625234 | + | 0.780437i | \(0.285004\pi\) | |||||||
\(84\) | −3.73205 | −0.407200 | ||||||||
\(85\) | −0.267949 | −0.0290632 | ||||||||
\(86\) | 6.73205 | 0.725936 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3923 | −1.73758 | −0.868790 | − | 0.495180i | \(-0.835102\pi\) | ||||
−0.868790 | + | 0.495180i | \(0.835102\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 11.1962 | 1.17368 | ||||||||
\(92\) | −4.73205 | −0.493350 | ||||||||
\(93\) | 8.19615 | 0.849901 | ||||||||
\(94\) | −8.92820 | −0.920874 | ||||||||
\(95\) | 4.46410 | 0.458007 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −18.7321 | −1.90195 | −0.950976 | − | 0.309265i | \(-0.899917\pi\) | ||||
−0.950976 | + | 0.309265i | \(0.899917\pi\) | |||||||
\(98\) | −6.92820 | −0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.53590 | 0.550842 | 0.275421 | − | 0.961324i | \(-0.411183\pi\) | ||||
0.275421 | + | 0.961324i | \(0.411183\pi\) | |||||||
\(102\) | 0.267949 | 0.0265309 | ||||||||
\(103\) | −18.3205 | −1.80517 | −0.902587 | − | 0.430508i | \(-0.858334\pi\) | ||||
−0.902587 | + | 0.430508i | \(0.858334\pi\) | |||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | −3.73205 | −0.364211 | ||||||||
\(106\) | 5.26795 | 0.511668 | ||||||||
\(107\) | −11.4641 | −1.10828 | −0.554138 | − | 0.832425i | \(-0.686952\pi\) | ||||
−0.554138 | + | 0.832425i | \(0.686952\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −13.4641 | −1.28963 | −0.644814 | − | 0.764340i | \(-0.723065\pi\) | ||||
−0.644814 | + | 0.764340i | \(0.723065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.73205 | −0.164399 | ||||||||
\(112\) | −3.73205 | −0.352646 | ||||||||
\(113\) | 13.8564 | 1.30350 | 0.651751 | − | 0.758433i | \(-0.274035\pi\) | ||||
0.651751 | + | 0.758433i | \(0.274035\pi\) | |||||||
\(114\) | −4.46410 | −0.418101 | ||||||||
\(115\) | −4.73205 | −0.441266 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | −3.00000 | −0.277350 | ||||||||
\(118\) | 4.19615 | 0.386287 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.19615 | −0.198830 | ||||||||
\(123\) | −4.73205 | −0.426675 | ||||||||
\(124\) | 8.19615 | 0.736036 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.73205 | 0.332478 | ||||||||
\(127\) | 0.392305 | 0.0348114 | 0.0174057 | − | 0.999849i | \(-0.494459\pi\) | ||||
0.0174057 | + | 0.999849i | \(0.494459\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.73205 | −0.592724 | ||||||||
\(130\) | 3.00000 | 0.263117 | ||||||||
\(131\) | −11.6603 | −1.01876 | −0.509381 | − | 0.860541i | \(-0.670125\pi\) | ||||
−0.509381 | + | 0.860541i | \(0.670125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.6603 | −1.44463 | ||||||||
\(134\) | 11.4641 | 0.990348 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0.267949 | 0.0229765 | ||||||||
\(137\) | −19.7846 | −1.69031 | −0.845157 | − | 0.534519i | \(-0.820493\pi\) | ||||
−0.845157 | + | 0.534519i | \(0.820493\pi\) | |||||||
\(138\) | 4.73205 | 0.402819 | ||||||||
\(139\) | −20.3205 | −1.72356 | −0.861781 | − | 0.507280i | \(-0.830651\pi\) | ||||
−0.861781 | + | 0.507280i | \(0.830651\pi\) | |||||||
\(140\) | −3.73205 | −0.315416 | ||||||||
\(141\) | 8.92820 | 0.751890 | ||||||||
\(142\) | 9.92820 | 0.833156 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.00000 | 0.249136 | ||||||||
\(146\) | 6.19615 | 0.512797 | ||||||||
\(147\) | 6.92820 | 0.571429 | ||||||||
\(148\) | −1.73205 | −0.142374 | ||||||||
\(149\) | 0.392305 | 0.0321389 | 0.0160694 | − | 0.999871i | \(-0.494885\pi\) | ||||
0.0160694 | + | 0.999871i | \(0.494885\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −13.2679 | −1.07973 | −0.539865 | − | 0.841751i | \(-0.681525\pi\) | ||||
−0.539865 | + | 0.841751i | \(0.681525\pi\) | |||||||
\(152\) | −4.46410 | −0.362086 | ||||||||
\(153\) | −0.267949 | −0.0216624 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.19615 | 0.658331 | ||||||||
\(156\) | −3.00000 | −0.240192 | ||||||||
\(157\) | 13.1962 | 1.05317 | 0.526584 | − | 0.850123i | \(-0.323473\pi\) | ||||
0.526584 | + | 0.850123i | \(0.323473\pi\) | |||||||
\(158\) | 0.535898 | 0.0426338 | ||||||||
\(159\) | −5.26795 | −0.417776 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 17.6603 | 1.39182 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 18.0526 | 1.41399 | 0.706993 | − | 0.707221i | \(-0.250051\pi\) | ||||
0.706993 | + | 0.707221i | \(0.250051\pi\) | |||||||
\(164\) | −4.73205 | −0.369511 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.3923 | −0.884214 | ||||||||
\(167\) | 21.4641 | 1.66094 | 0.830471 | − | 0.557062i | \(-0.188071\pi\) | ||||
0.830471 | + | 0.557062i | \(0.188071\pi\) | |||||||
\(168\) | 3.73205 | 0.287934 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0.267949 | 0.0205508 | ||||||||
\(171\) | 4.46410 | 0.341378 | ||||||||
\(172\) | −6.73205 | −0.513314 | ||||||||
\(173\) | −14.5885 | −1.10914 | −0.554570 | − | 0.832137i | \(-0.687117\pi\) | ||||
−0.554570 | + | 0.832137i | \(0.687117\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | −3.73205 | −0.282117 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.19615 | −0.315402 | ||||||||
\(178\) | 16.3923 | 1.22866 | ||||||||
\(179\) | 7.12436 | 0.532499 | 0.266250 | − | 0.963904i | \(-0.414215\pi\) | ||||
0.266250 | + | 0.963904i | \(0.414215\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 4.19615 | 0.311898 | 0.155949 | − | 0.987765i | \(-0.450157\pi\) | ||||
0.155949 | + | 0.987765i | \(0.450157\pi\) | |||||||
\(182\) | −11.1962 | −0.829914 | ||||||||
\(183\) | 2.19615 | 0.162344 | ||||||||
\(184\) | 4.73205 | 0.348851 | ||||||||
\(185\) | −1.73205 | −0.127343 | ||||||||
\(186\) | −8.19615 | −0.600971 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.92820 | 0.651156 | ||||||||
\(189\) | −3.73205 | −0.271467 | ||||||||
\(190\) | −4.46410 | −0.323860 | ||||||||
\(191\) | 18.4641 | 1.33602 | 0.668008 | − | 0.744154i | \(-0.267147\pi\) | ||||
0.668008 | + | 0.744154i | \(0.267147\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −9.46410 | −0.681241 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(194\) | 18.7321 | 1.34488 | ||||||||
\(195\) | −3.00000 | −0.214834 | ||||||||
\(196\) | 6.92820 | 0.494872 | ||||||||
\(197\) | 13.4641 | 0.959278 | 0.479639 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479639 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3923 | −1.16202 | −0.581010 | − | 0.813897i | \(-0.697342\pi\) | ||||
−0.581010 | + | 0.813897i | \(0.697342\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −11.4641 | −0.808615 | ||||||||
\(202\) | −5.53590 | −0.389504 | ||||||||
\(203\) | −11.1962 | −0.785816 | ||||||||
\(204\) | −0.267949 | −0.0187602 | ||||||||
\(205\) | −4.73205 | −0.330501 | ||||||||
\(206\) | 18.3205 | 1.27645 | ||||||||
\(207\) | −4.73205 | −0.328900 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.73205 | 0.257536 | ||||||||
\(211\) | −17.7846 | −1.22434 | −0.612172 | − | 0.790725i | \(-0.709704\pi\) | ||||
−0.612172 | + | 0.790725i | \(0.709704\pi\) | |||||||
\(212\) | −5.26795 | −0.361804 | ||||||||
\(213\) | −9.92820 | −0.680269 | ||||||||
\(214\) | 11.4641 | 0.783670 | ||||||||
\(215\) | −6.73205 | −0.459122 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −30.5885 | −2.07648 | ||||||||
\(218\) | 13.4641 | 0.911904 | ||||||||
\(219\) | −6.19615 | −0.418697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.803848 | 0.0540726 | ||||||||
\(222\) | 1.73205 | 0.116248 | ||||||||
\(223\) | 6.46410 | 0.432868 | 0.216434 | − | 0.976297i | \(-0.430557\pi\) | ||||
0.216434 | + | 0.976297i | \(0.430557\pi\) | |||||||
\(224\) | 3.73205 | 0.249358 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −13.8564 | −0.921714 | ||||||||
\(227\) | 10.3923 | 0.689761 | 0.344881 | − | 0.938647i | \(-0.387919\pi\) | ||||
0.344881 | + | 0.938647i | \(0.387919\pi\) | |||||||
\(228\) | 4.46410 | 0.295642 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 4.73205 | 0.312022 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | −1.85641 | −0.121617 | −0.0608086 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608086 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(234\) | 3.00000 | 0.196116 | ||||||||
\(235\) | 8.92820 | 0.582412 | ||||||||
\(236\) | −4.19615 | −0.273146 | ||||||||
\(237\) | −0.535898 | −0.0348103 | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | 6.26795 | 0.405440 | 0.202720 | − | 0.979237i | \(-0.435022\pi\) | ||||
0.202720 | + | 0.979237i | \(0.435022\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 22.6603 | 1.45968 | 0.729838 | − | 0.683621i | \(-0.239596\pi\) | ||||
0.729838 | + | 0.683621i | \(0.239596\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.19615 | 0.140594 | ||||||||
\(245\) | 6.92820 | 0.442627 | ||||||||
\(246\) | 4.73205 | 0.301705 | ||||||||
\(247\) | −13.3923 | −0.852132 | ||||||||
\(248\) | −8.19615 | −0.520456 | ||||||||
\(249\) | 11.3923 | 0.721958 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 18.5359 | 1.16998 | 0.584988 | − | 0.811042i | \(-0.301099\pi\) | ||||
0.584988 | + | 0.811042i | \(0.301099\pi\) | |||||||
\(252\) | −3.73205 | −0.235097 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.392305 | −0.0246154 | ||||||||
\(255\) | −0.267949 | −0.0167796 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.32051 | 0.394262 | 0.197131 | − | 0.980377i | \(-0.436837\pi\) | ||||
0.197131 | + | 0.980377i | \(0.436837\pi\) | |||||||
\(258\) | 6.73205 | 0.419119 | ||||||||
\(259\) | 6.46410 | 0.401660 | ||||||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | 11.6603 | 0.720373 | ||||||||
\(263\) | 25.1244 | 1.54923 | 0.774617 | − | 0.632431i | \(-0.217943\pi\) | ||||
0.774617 | + | 0.632431i | \(0.217943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.26795 | −0.323608 | ||||||||
\(266\) | 16.6603 | 1.02151 | ||||||||
\(267\) | −16.3923 | −1.00319 | ||||||||
\(268\) | −11.4641 | −0.700281 | ||||||||
\(269\) | 11.5885 | 0.706561 | 0.353280 | − | 0.935517i | \(-0.385066\pi\) | ||||
0.353280 | + | 0.935517i | \(0.385066\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 23.8564 | 1.44917 | 0.724587 | − | 0.689184i | \(-0.242031\pi\) | ||||
0.724587 | + | 0.689184i | \(0.242031\pi\) | |||||||
\(272\) | −0.267949 | −0.0162468 | ||||||||
\(273\) | 11.1962 | 0.677622 | ||||||||
\(274\) | 19.7846 | 1.19523 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.73205 | −0.284836 | ||||||||
\(277\) | −18.9282 | −1.13729 | −0.568643 | − | 0.822585i | \(-0.692531\pi\) | ||||
−0.568643 | + | 0.822585i | \(0.692531\pi\) | |||||||
\(278\) | 20.3205 | 1.21874 | ||||||||
\(279\) | 8.19615 | 0.490691 | ||||||||
\(280\) | 3.73205 | 0.223033 | ||||||||
\(281\) | −26.0526 | −1.55417 | −0.777083 | − | 0.629399i | \(-0.783301\pi\) | ||||
−0.777083 | + | 0.629399i | \(0.783301\pi\) | |||||||
\(282\) | −8.92820 | −0.531667 | ||||||||
\(283\) | 30.2487 | 1.79810 | 0.899050 | − | 0.437847i | \(-0.144259\pi\) | ||||
0.899050 | + | 0.437847i | \(0.144259\pi\) | |||||||
\(284\) | −9.92820 | −0.589130 | ||||||||
\(285\) | 4.46410 | 0.264431 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.6603 | 1.04245 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9282 | −0.995777 | ||||||||
\(290\) | −3.00000 | −0.176166 | ||||||||
\(291\) | −18.7321 | −1.09809 | ||||||||
\(292\) | −6.19615 | −0.362602 | ||||||||
\(293\) | 18.9282 | 1.10580 | 0.552899 | − | 0.833248i | \(-0.313522\pi\) | ||||
0.552899 | + | 0.833248i | \(0.313522\pi\) | |||||||
\(294\) | −6.92820 | −0.404061 | ||||||||
\(295\) | −4.19615 | −0.244309 | ||||||||
\(296\) | 1.73205 | 0.100673 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.392305 | −0.0227256 | ||||||||
\(299\) | 14.1962 | 0.820985 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 25.1244 | 1.44814 | ||||||||
\(302\) | 13.2679 | 0.763485 | ||||||||
\(303\) | 5.53590 | 0.318029 | ||||||||
\(304\) | 4.46410 | 0.256034 | ||||||||
\(305\) | 2.19615 | 0.125751 | ||||||||
\(306\) | 0.267949 | 0.0153176 | ||||||||
\(307\) | −6.73205 | −0.384218 | −0.192109 | − | 0.981374i | \(-0.561533\pi\) | ||||
−0.192109 | + | 0.981374i | \(0.561533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3205 | −1.04222 | ||||||||
\(310\) | −8.19615 | −0.465510 | ||||||||
\(311\) | 13.8564 | 0.785725 | 0.392862 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392862 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(312\) | 3.00000 | 0.169842 | ||||||||
\(313\) | −19.1244 | −1.08097 | −0.540486 | − | 0.841353i | \(-0.681760\pi\) | ||||
−0.540486 | + | 0.841353i | \(0.681760\pi\) | |||||||
\(314\) | −13.1962 | −0.744702 | ||||||||
\(315\) | −3.73205 | −0.210277 | ||||||||
\(316\) | −0.535898 | −0.0301466 | ||||||||
\(317\) | −15.1244 | −0.849468 | −0.424734 | − | 0.905318i | \(-0.639632\pi\) | ||||
−0.424734 | + | 0.905318i | \(0.639632\pi\) | |||||||
\(318\) | 5.26795 | 0.295412 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −11.4641 | −0.639864 | ||||||||
\(322\) | −17.6603 | −0.984167 | ||||||||
\(323\) | −1.19615 | −0.0665557 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.00000 | −0.166410 | ||||||||
\(326\) | −18.0526 | −0.999839 | ||||||||
\(327\) | −13.4641 | −0.744567 | ||||||||
\(328\) | 4.73205 | 0.261284 | ||||||||
\(329\) | −33.3205 | −1.83702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.5167 | −1.67735 | −0.838674 | − | 0.544634i | \(-0.816668\pi\) | ||||
−0.838674 | + | 0.544634i | \(0.816668\pi\) | |||||||
\(332\) | 11.3923 | 0.625234 | ||||||||
\(333\) | −1.73205 | −0.0949158 | ||||||||
\(334\) | −21.4641 | −1.17446 | ||||||||
\(335\) | −11.4641 | −0.626351 | ||||||||
\(336\) | −3.73205 | −0.203600 | ||||||||
\(337\) | −23.2679 | −1.26749 | −0.633743 | − | 0.773544i | \(-0.718482\pi\) | ||||
−0.633743 | + | 0.773544i | \(0.718482\pi\) | |||||||
\(338\) | 4.00000 | 0.217571 | ||||||||
\(339\) | 13.8564 | 0.752577 | ||||||||
\(340\) | −0.267949 | −0.0145316 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.46410 | −0.241391 | ||||||||
\(343\) | 0.267949 | 0.0144679 | ||||||||
\(344\) | 6.73205 | 0.362968 | ||||||||
\(345\) | −4.73205 | −0.254765 | ||||||||
\(346\) | 14.5885 | 0.784280 | ||||||||
\(347\) | −25.3923 | −1.36313 | −0.681565 | − | 0.731757i | \(-0.738700\pi\) | ||||
−0.681565 | + | 0.731757i | \(0.738700\pi\) | |||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | −7.85641 | −0.420544 | −0.210272 | − | 0.977643i | \(-0.567435\pi\) | ||||
−0.210272 | + | 0.977643i | \(0.567435\pi\) | |||||||
\(350\) | 3.73205 | 0.199487 | ||||||||
\(351\) | −3.00000 | −0.160128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.92820 | 0.368751 | 0.184376 | − | 0.982856i | \(-0.440974\pi\) | ||||
0.184376 | + | 0.982856i | \(0.440974\pi\) | |||||||
\(354\) | 4.19615 | 0.223023 | ||||||||
\(355\) | −9.92820 | −0.526934 | ||||||||
\(356\) | −16.3923 | −0.868790 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | −7.12436 | −0.376534 | ||||||||
\(359\) | 27.4641 | 1.44950 | 0.724750 | − | 0.689012i | \(-0.241955\pi\) | ||||
0.724750 | + | 0.689012i | \(0.241955\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | −4.19615 | −0.220545 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.1962 | 0.586838 | ||||||||
\(365\) | −6.19615 | −0.324321 | ||||||||
\(366\) | −2.19615 | −0.114795 | ||||||||
\(367\) | 14.8564 | 0.775498 | 0.387749 | − | 0.921765i | \(-0.373253\pi\) | ||||
0.387749 | + | 0.921765i | \(0.373253\pi\) | |||||||
\(368\) | −4.73205 | −0.246675 | ||||||||
\(369\) | −4.73205 | −0.246341 | ||||||||
\(370\) | 1.73205 | 0.0900450 | ||||||||
\(371\) | 19.6603 | 1.02071 | ||||||||
\(372\) | 8.19615 | 0.424951 | ||||||||
\(373\) | −6.07180 | −0.314386 | −0.157193 | − | 0.987568i | \(-0.550244\pi\) | ||||
−0.157193 | + | 0.987568i | \(0.550244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −8.92820 | −0.460437 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 3.73205 | 0.191956 | ||||||||
\(379\) | 21.4449 | 1.10155 | 0.550774 | − | 0.834654i | \(-0.314332\pi\) | ||||
0.550774 | + | 0.834654i | \(0.314332\pi\) | |||||||
\(380\) | 4.46410 | 0.229004 | ||||||||
\(381\) | 0.392305 | 0.0200984 | ||||||||
\(382\) | −18.4641 | −0.944706 | ||||||||
\(383\) | −16.9282 | −0.864991 | −0.432495 | − | 0.901636i | \(-0.642367\pi\) | ||||
−0.432495 | + | 0.901636i | \(0.642367\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.46410 | 0.481710 | ||||||||
\(387\) | −6.73205 | −0.342209 | ||||||||
\(388\) | −18.7321 | −0.950976 | ||||||||
\(389\) | −37.8564 | −1.91940 | −0.959698 | − | 0.281033i | \(-0.909323\pi\) | ||||
−0.959698 | + | 0.281033i | \(0.909323\pi\) | |||||||
\(390\) | 3.00000 | 0.151911 | ||||||||
\(391\) | 1.26795 | 0.0641229 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | −11.6603 | −0.588182 | ||||||||
\(394\) | −13.4641 | −0.678312 | ||||||||
\(395\) | −0.535898 | −0.0269640 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.9808 | 1.30394 | 0.651969 | − | 0.758246i | \(-0.273943\pi\) | ||||
0.651969 | + | 0.758246i | \(0.273943\pi\) | |||||||
\(398\) | 16.3923 | 0.821672 | ||||||||
\(399\) | −16.6603 | −0.834056 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 17.6603 | 0.881911 | 0.440956 | − | 0.897529i | \(-0.354640\pi\) | ||||
0.440956 | + | 0.897529i | \(0.354640\pi\) | |||||||
\(402\) | 11.4641 | 0.571777 | ||||||||
\(403\) | −24.5885 | −1.22484 | ||||||||
\(404\) | 5.53590 | 0.275421 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 11.1962 | 0.555656 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.267949 | 0.0132655 | ||||||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 4.73205 | 0.233699 | ||||||||
\(411\) | −19.7846 | −0.975903 | ||||||||
\(412\) | −18.3205 | −0.902587 | ||||||||
\(413\) | 15.6603 | 0.770591 | ||||||||
\(414\) | 4.73205 | 0.232568 | ||||||||
\(415\) | 11.3923 | 0.559226 | ||||||||
\(416\) | 3.00000 | 0.147087 | ||||||||
\(417\) | −20.3205 | −0.995100 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.4641 | −0.560058 | −0.280029 | − | 0.959992i | \(-0.590344\pi\) | ||||
−0.280029 | + | 0.959992i | \(0.590344\pi\) | |||||||
\(420\) | −3.73205 | −0.182105 | ||||||||
\(421\) | −4.05256 | −0.197510 | −0.0987548 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987548 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(422\) | 17.7846 | 0.865741 | ||||||||
\(423\) | 8.92820 | 0.434104 | ||||||||
\(424\) | 5.26795 | 0.255834 | ||||||||
\(425\) | −0.267949 | −0.0129974 | ||||||||
\(426\) | 9.92820 | 0.481023 | ||||||||
\(427\) | −8.19615 | −0.396640 | ||||||||
\(428\) | −11.4641 | −0.554138 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.73205 | 0.324648 | ||||||||
\(431\) | −6.12436 | −0.295000 | −0.147500 | − | 0.989062i | \(-0.547123\pi\) | ||||
−0.147500 | + | 0.989062i | \(0.547123\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −10.9282 | −0.525176 | −0.262588 | − | 0.964908i | \(-0.584576\pi\) | ||||
−0.262588 | + | 0.964908i | \(0.584576\pi\) | |||||||
\(434\) | 30.5885 | 1.46829 | ||||||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | −13.4641 | −0.644814 | ||||||||
\(437\) | −21.1244 | −1.01051 | ||||||||
\(438\) | 6.19615 | 0.296064 | ||||||||
\(439\) | −4.92820 | −0.235210 | −0.117605 | − | 0.993060i | \(-0.537522\pi\) | ||||
−0.117605 | + | 0.993060i | \(0.537522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.92820 | 0.329914 | ||||||||
\(442\) | −0.803848 | −0.0382351 | ||||||||
\(443\) | −5.19615 | −0.246877 | −0.123438 | − | 0.992352i | \(-0.539392\pi\) | ||||
−0.123438 | + | 0.992352i | \(0.539392\pi\) | |||||||
\(444\) | −1.73205 | −0.0821995 | ||||||||
\(445\) | −16.3923 | −0.777070 | ||||||||
\(446\) | −6.46410 | −0.306084 | ||||||||
\(447\) | 0.392305 | 0.0185554 | ||||||||
\(448\) | −3.73205 | −0.176323 | ||||||||
\(449\) | −3.46410 | −0.163481 | −0.0817405 | − | 0.996654i | \(-0.526048\pi\) | ||||
−0.0817405 | + | 0.996654i | \(0.526048\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.8564 | 0.651751 | ||||||||
\(453\) | −13.2679 | −0.623383 | ||||||||
\(454\) | −10.3923 | −0.487735 | ||||||||
\(455\) | 11.1962 | 0.524884 | ||||||||
\(456\) | −4.46410 | −0.209051 | ||||||||
\(457\) | 30.4449 | 1.42415 | 0.712075 | − | 0.702103i | \(-0.247755\pi\) | ||||
0.712075 | + | 0.702103i | \(0.247755\pi\) | |||||||
\(458\) | 12.0000 | 0.560723 | ||||||||
\(459\) | −0.267949 | −0.0125068 | ||||||||
\(460\) | −4.73205 | −0.220633 | ||||||||
\(461\) | 17.2487 | 0.803353 | 0.401676 | − | 0.915782i | \(-0.368428\pi\) | ||||
0.401676 | + | 0.915782i | \(0.368428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4641 | −0.532782 | −0.266391 | − | 0.963865i | \(-0.585831\pi\) | ||||
−0.266391 | + | 0.963865i | \(0.585831\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 8.19615 | 0.380087 | ||||||||
\(466\) | 1.85641 | 0.0859964 | ||||||||
\(467\) | −30.1244 | −1.39399 | −0.696994 | − | 0.717077i | \(-0.745480\pi\) | ||||
−0.696994 | + | 0.717077i | \(0.745480\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | 42.7846 | 1.97561 | ||||||||
\(470\) | −8.92820 | −0.411827 | ||||||||
\(471\) | 13.1962 | 0.608047 | ||||||||
\(472\) | 4.19615 | 0.193144 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.535898 | 0.0246146 | ||||||||
\(475\) | 4.46410 | 0.204827 | ||||||||
\(476\) | 1.00000 | 0.0458349 | ||||||||
\(477\) | −5.26795 | −0.241203 | ||||||||
\(478\) | −6.26795 | −0.286689 | ||||||||
\(479\) | 8.26795 | 0.377772 | 0.188886 | − | 0.981999i | \(-0.439512\pi\) | ||||
0.188886 | + | 0.981999i | \(0.439512\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 5.19615 | 0.236924 | ||||||||
\(482\) | −22.6603 | −1.03215 | ||||||||
\(483\) | 17.6603 | 0.803569 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.7321 | −0.850579 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 6.46410 | 0.292916 | 0.146458 | − | 0.989217i | \(-0.453213\pi\) | ||||
0.146458 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(488\) | −2.19615 | −0.0994151 | ||||||||
\(489\) | 18.0526 | 0.816365 | ||||||||
\(490\) | −6.92820 | −0.312984 | ||||||||
\(491\) | −1.26795 | −0.0572217 | −0.0286109 | − | 0.999591i | \(-0.509108\pi\) | ||||
−0.0286109 | + | 0.999591i | \(0.509108\pi\) | |||||||
\(492\) | −4.73205 | −0.213337 | ||||||||
\(493\) | −0.803848 | −0.0362035 | ||||||||
\(494\) | 13.3923 | 0.602548 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.19615 | 0.368018 | ||||||||
\(497\) | 37.0526 | 1.66203 | ||||||||
\(498\) | −11.3923 | −0.510501 | ||||||||
\(499\) | −21.4449 | −0.960004 | −0.480002 | − | 0.877267i | \(-0.659364\pi\) | ||||
−0.480002 | + | 0.877267i | \(0.659364\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 21.4641 | 0.958945 | ||||||||
\(502\) | −18.5359 | −0.827298 | ||||||||
\(503\) | 17.2679 | 0.769940 | 0.384970 | − | 0.922929i | \(-0.374212\pi\) | ||||
0.384970 | + | 0.922929i | \(0.374212\pi\) | |||||||
\(504\) | 3.73205 | 0.166239 | ||||||||
\(505\) | 5.53590 | 0.246344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.00000 | −0.177646 | ||||||||
\(508\) | 0.392305 | 0.0174057 | ||||||||
\(509\) | −8.14359 | −0.360958 | −0.180479 | − | 0.983579i | \(-0.557765\pi\) | ||||
−0.180479 | + | 0.983579i | \(0.557765\pi\) | |||||||
\(510\) | 0.267949 | 0.0118650 | ||||||||
\(511\) | 23.1244 | 1.02296 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.46410 | 0.197095 | ||||||||
\(514\) | −6.32051 | −0.278786 | ||||||||
\(515\) | −18.3205 | −0.807298 | ||||||||
\(516\) | −6.73205 | −0.296362 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.46410 | −0.284016 | ||||||||
\(519\) | −14.5885 | −0.640362 | ||||||||
\(520\) | 3.00000 | 0.131559 | ||||||||
\(521\) | −22.5885 | −0.989618 | −0.494809 | − | 0.869002i | \(-0.664762\pi\) | ||||
−0.494809 | + | 0.869002i | \(0.664762\pi\) | |||||||
\(522\) | −3.00000 | −0.131306 | ||||||||
\(523\) | 19.2679 | 0.842529 | 0.421264 | − | 0.906938i | \(-0.361586\pi\) | ||||
0.421264 | + | 0.906938i | \(0.361586\pi\) | |||||||
\(524\) | −11.6603 | −0.509381 | ||||||||
\(525\) | −3.73205 | −0.162880 | ||||||||
\(526\) | −25.1244 | −1.09547 | ||||||||
\(527\) | −2.19615 | −0.0956659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 5.26795 | 0.228825 | ||||||||
\(531\) | −4.19615 | −0.182098 | ||||||||
\(532\) | −16.6603 | −0.722314 | ||||||||
\(533\) | 14.1962 | 0.614904 | ||||||||
\(534\) | 16.3923 | 0.709364 | ||||||||
\(535\) | −11.4641 | −0.495636 | ||||||||
\(536\) | 11.4641 | 0.495174 | ||||||||
\(537\) | 7.12436 | 0.307439 | ||||||||
\(538\) | −11.5885 | −0.499614 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −8.58846 | −0.369247 | −0.184623 | − | 0.982809i | \(-0.559107\pi\) | ||||
−0.184623 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(542\) | −23.8564 | −1.02472 | ||||||||
\(543\) | 4.19615 | 0.180074 | ||||||||
\(544\) | 0.267949 | 0.0114882 | ||||||||
\(545\) | −13.4641 | −0.576739 | ||||||||
\(546\) | −11.1962 | −0.479151 | ||||||||
\(547\) | −15.0718 | −0.644423 | −0.322212 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322212 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(548\) | −19.7846 | −0.845157 | ||||||||
\(549\) | 2.19615 | 0.0937295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3923 | 0.570531 | ||||||||
\(552\) | 4.73205 | 0.201409 | ||||||||
\(553\) | 2.00000 | 0.0850487 | ||||||||
\(554\) | 18.9282 | 0.804182 | ||||||||
\(555\) | −1.73205 | −0.0735215 | ||||||||
\(556\) | −20.3205 | −0.861781 | ||||||||
\(557\) | 10.3923 | 0.440336 | 0.220168 | − | 0.975462i | \(-0.429339\pi\) | ||||
0.220168 | + | 0.975462i | \(0.429339\pi\) | |||||||
\(558\) | −8.19615 | −0.346971 | ||||||||
\(559\) | 20.1962 | 0.854206 | ||||||||
\(560\) | −3.73205 | −0.157708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.0526 | 1.09896 | ||||||||
\(563\) | −41.1051 | −1.73237 | −0.866187 | − | 0.499720i | \(-0.833436\pi\) | ||||
−0.866187 | + | 0.499720i | \(0.833436\pi\) | |||||||
\(564\) | 8.92820 | 0.375945 | ||||||||
\(565\) | 13.8564 | 0.582943 | ||||||||
\(566\) | −30.2487 | −1.27145 | ||||||||
\(567\) | −3.73205 | −0.156731 | ||||||||
\(568\) | 9.92820 | 0.416578 | ||||||||
\(569\) | 25.8038 | 1.08175 | 0.540877 | − | 0.841102i | \(-0.318093\pi\) | ||||
0.540877 | + | 0.841102i | \(0.318093\pi\) | |||||||
\(570\) | −4.46410 | −0.186981 | ||||||||
\(571\) | 45.3205 | 1.89660 | 0.948302 | − | 0.317369i | \(-0.102799\pi\) | ||||
0.948302 | + | 0.317369i | \(0.102799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.4641 | 0.771349 | ||||||||
\(574\) | −17.6603 | −0.737125 | ||||||||
\(575\) | −4.73205 | −0.197340 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.3205 | −0.721062 | −0.360531 | − | 0.932747i | \(-0.617405\pi\) | ||||
−0.360531 | + | 0.932747i | \(0.617405\pi\) | |||||||
\(578\) | 16.9282 | 0.704120 | ||||||||
\(579\) | −9.46410 | −0.393315 | ||||||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | −42.5167 | −1.76389 | ||||||||
\(582\) | 18.7321 | 0.776468 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.19615 | 0.256399 | ||||||||
\(585\) | −3.00000 | −0.124035 | ||||||||
\(586\) | −18.9282 | −0.781917 | ||||||||
\(587\) | 22.9090 | 0.945554 | 0.472777 | − | 0.881182i | \(-0.343252\pi\) | ||||
0.472777 | + | 0.881182i | \(0.343252\pi\) | |||||||
\(588\) | 6.92820 | 0.285714 | ||||||||
\(589\) | 36.5885 | 1.50760 | ||||||||
\(590\) | 4.19615 | 0.172753 | ||||||||
\(591\) | 13.4641 | 0.553839 | ||||||||
\(592\) | −1.73205 | −0.0711868 | ||||||||
\(593\) | 4.92820 | 0.202377 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.00000 | 0.0409960 | ||||||||
\(596\) | 0.392305 | 0.0160694 | ||||||||
\(597\) | −16.3923 | −0.670892 | ||||||||
\(598\) | −14.1962 | −0.580524 | ||||||||
\(599\) | −34.3923 | −1.40523 | −0.702616 | − | 0.711569i | \(-0.747985\pi\) | ||||
−0.702616 | + | 0.711569i | \(0.747985\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −39.8564 | −1.62578 | −0.812888 | − | 0.582420i | \(-0.802106\pi\) | ||||
−0.812888 | + | 0.582420i | \(0.802106\pi\) | |||||||
\(602\) | −25.1244 | −1.02399 | ||||||||
\(603\) | −11.4641 | −0.466854 | ||||||||
\(604\) | −13.2679 | −0.539865 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.53590 | −0.224880 | ||||||||
\(607\) | −8.41154 | −0.341414 | −0.170707 | − | 0.985322i | \(-0.554605\pi\) | ||||
−0.170707 | + | 0.985322i | \(0.554605\pi\) | |||||||
\(608\) | −4.46410 | −0.181043 | ||||||||
\(609\) | −11.1962 | −0.453691 | ||||||||
\(610\) | −2.19615 | −0.0889196 | ||||||||
\(611\) | −26.7846 | −1.08359 | ||||||||
\(612\) | −0.267949 | −0.0108312 | ||||||||
\(613\) | −33.6410 | −1.35875 | −0.679374 | − | 0.733792i | \(-0.737749\pi\) | ||||
−0.679374 | + | 0.733792i | \(0.737749\pi\) | |||||||
\(614\) | 6.73205 | 0.271683 | ||||||||
\(615\) | −4.73205 | −0.190815 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.7846 | 1.11857 | 0.559283 | − | 0.828977i | \(-0.311076\pi\) | ||||
0.559283 | + | 0.828977i | \(0.311076\pi\) | |||||||
\(618\) | 18.3205 | 0.736959 | ||||||||
\(619\) | −19.9808 | −0.803095 | −0.401547 | − | 0.915838i | \(-0.631527\pi\) | ||||
−0.401547 | + | 0.915838i | \(0.631527\pi\) | |||||||
\(620\) | 8.19615 | 0.329165 | ||||||||
\(621\) | −4.73205 | −0.189891 | ||||||||
\(622\) | −13.8564 | −0.555591 | ||||||||
\(623\) | 61.1769 | 2.45100 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.1244 | 0.764363 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.1962 | 0.526584 | ||||||||
\(629\) | 0.464102 | 0.0185049 | ||||||||
\(630\) | 3.73205 | 0.148688 | ||||||||
\(631\) | 17.8038 | 0.708760 | 0.354380 | − | 0.935102i | \(-0.384692\pi\) | ||||
0.354380 | + | 0.935102i | \(0.384692\pi\) | |||||||
\(632\) | 0.535898 | 0.0213169 | ||||||||
\(633\) | −17.7846 | −0.706875 | ||||||||
\(634\) | 15.1244 | 0.600665 | ||||||||
\(635\) | 0.392305 | 0.0155681 | ||||||||
\(636\) | −5.26795 | −0.208888 | ||||||||
\(637\) | −20.7846 | −0.823516 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.92820 | −0.392754 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 8.92820 | 0.352643 | 0.176321 | − | 0.984333i | \(-0.443580\pi\) | ||||
0.176321 | + | 0.984333i | \(0.443580\pi\) | |||||||
\(642\) | 11.4641 | 0.452452 | ||||||||
\(643\) | 37.8564 | 1.49291 | 0.746455 | − | 0.665435i | \(-0.231754\pi\) | ||||
0.746455 | + | 0.665435i | \(0.231754\pi\) | |||||||
\(644\) | 17.6603 | 0.695911 | ||||||||
\(645\) | −6.73205 | −0.265074 | ||||||||
\(646\) | 1.19615 | 0.0470620 | ||||||||
\(647\) | 8.67949 | 0.341226 | 0.170613 | − | 0.985338i | \(-0.445425\pi\) | ||||
0.170613 | + | 0.985338i | \(0.445425\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.00000 | 0.117670 | ||||||||
\(651\) | −30.5885 | −1.19886 | ||||||||
\(652\) | 18.0526 | 0.706993 | ||||||||
\(653\) | −26.1962 | −1.02513 | −0.512567 | − | 0.858647i | \(-0.671306\pi\) | ||||
−0.512567 | + | 0.858647i | \(0.671306\pi\) | |||||||
\(654\) | 13.4641 | 0.526488 | ||||||||
\(655\) | −11.6603 | −0.455604 | ||||||||
\(656\) | −4.73205 | −0.184756 | ||||||||
\(657\) | −6.19615 | −0.241735 | ||||||||
\(658\) | 33.3205 | 1.29897 | ||||||||
\(659\) | −18.3923 | −0.716462 | −0.358231 | − | 0.933633i | \(-0.616620\pi\) | ||||
−0.358231 | + | 0.933633i | \(0.616620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.1962 | −0.707748 | −0.353874 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353874 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(662\) | 30.5167 | 1.18606 | ||||||||
\(663\) | 0.803848 | 0.0312189 | ||||||||
\(664\) | −11.3923 | −0.442107 | ||||||||
\(665\) | −16.6603 | −0.646057 | ||||||||
\(666\) | 1.73205 | 0.0671156 | ||||||||
\(667\) | −14.1962 | −0.549677 | ||||||||
\(668\) | 21.4641 | 0.830471 | ||||||||
\(669\) | 6.46410 | 0.249917 | ||||||||
\(670\) | 11.4641 | 0.442897 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.73205 | 0.143967 | ||||||||
\(673\) | 17.8564 | 0.688314 | 0.344157 | − | 0.938912i | \(-0.388165\pi\) | ||||
0.344157 | + | 0.938912i | \(0.388165\pi\) | |||||||
\(674\) | 23.2679 | 0.896248 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 34.0526 | 1.30875 | 0.654373 | − | 0.756172i | \(-0.272933\pi\) | ||||
0.654373 | + | 0.756172i | \(0.272933\pi\) | |||||||
\(678\) | −13.8564 | −0.532152 | ||||||||
\(679\) | 69.9090 | 2.68286 | ||||||||
\(680\) | 0.267949 | 0.0102754 | ||||||||
\(681\) | 10.3923 | 0.398234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.87564 | −0.224825 | −0.112413 | − | 0.993662i | \(-0.535858\pi\) | ||||
−0.112413 | + | 0.993662i | \(0.535858\pi\) | |||||||
\(684\) | 4.46410 | 0.170689 | ||||||||
\(685\) | −19.7846 | −0.755931 | ||||||||
\(686\) | −0.267949 | −0.0102303 | ||||||||
\(687\) | −12.0000 | −0.457829 | ||||||||
\(688\) | −6.73205 | −0.256657 | ||||||||
\(689\) | 15.8038 | 0.602079 | ||||||||
\(690\) | 4.73205 | 0.180146 | ||||||||
\(691\) | 51.0526 | 1.94213 | 0.971065 | − | 0.238814i | \(-0.0767585\pi\) | ||||
0.971065 | + | 0.238814i | \(0.0767585\pi\) | |||||||
\(692\) | −14.5885 | −0.554570 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.3923 | 0.963879 | ||||||||
\(695\) | −20.3205 | −0.770801 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | 1.26795 | 0.0480270 | ||||||||
\(698\) | 7.85641 | 0.297369 | ||||||||
\(699\) | −1.85641 | −0.0702157 | ||||||||
\(700\) | −3.73205 | −0.141058 | ||||||||
\(701\) | 48.4641 | 1.83046 | 0.915232 | − | 0.402927i | \(-0.132007\pi\) | ||||
0.915232 | + | 0.402927i | \(0.132007\pi\) | |||||||
\(702\) | 3.00000 | 0.113228 | ||||||||
\(703\) | −7.73205 | −0.291620 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.92820 | 0.336256 | ||||||||
\(706\) | −6.92820 | −0.260746 | ||||||||
\(707\) | −20.6603 | −0.777009 | ||||||||
\(708\) | −4.19615 | −0.157701 | ||||||||
\(709\) | −4.33975 | −0.162983 | −0.0814913 | − | 0.996674i | \(-0.525968\pi\) | ||||
−0.0814913 | + | 0.996674i | \(0.525968\pi\) | |||||||
\(710\) | 9.92820 | 0.372599 | ||||||||
\(711\) | −0.535898 | −0.0200978 | ||||||||
\(712\) | 16.3923 | 0.614328 | ||||||||
\(713\) | −38.7846 | −1.45250 | ||||||||
\(714\) | −1.00000 | −0.0374241 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.12436 | 0.266250 | ||||||||
\(717\) | 6.26795 | 0.234081 | ||||||||
\(718\) | −27.4641 | −1.02495 | ||||||||
\(719\) | 24.5359 | 0.915035 | 0.457517 | − | 0.889201i | \(-0.348739\pi\) | ||||
0.457517 | + | 0.889201i | \(0.348739\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 68.3731 | 2.54635 | ||||||||
\(722\) | −0.928203 | −0.0345441 | ||||||||
\(723\) | 22.6603 | 0.842744 | ||||||||
\(724\) | 4.19615 | 0.155949 | ||||||||
\(725\) | 3.00000 | 0.111417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.4974 | 1.76158 | 0.880791 | − | 0.473505i | \(-0.157012\pi\) | ||||
0.880791 | + | 0.473505i | \(0.157012\pi\) | |||||||
\(728\) | −11.1962 | −0.414957 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.19615 | 0.229330 | ||||||||
\(731\) | 1.80385 | 0.0667177 | ||||||||
\(732\) | 2.19615 | 0.0811721 | ||||||||
\(733\) | −17.8564 | −0.659541 | −0.329771 | − | 0.944061i | \(-0.606971\pi\) | ||||
−0.329771 | + | 0.944061i | \(0.606971\pi\) | |||||||
\(734\) | −14.8564 | −0.548360 | ||||||||
\(735\) | 6.92820 | 0.255551 | ||||||||
\(736\) | 4.73205 | 0.174426 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.73205 | 0.174189 | ||||||||
\(739\) | −16.4641 | −0.605642 | −0.302821 | − | 0.953047i | \(-0.597928\pi\) | ||||
−0.302821 | + | 0.953047i | \(0.597928\pi\) | |||||||
\(740\) | −1.73205 | −0.0636715 | ||||||||
\(741\) | −13.3923 | −0.491979 | ||||||||
\(742\) | −19.6603 | −0.721751 | ||||||||
\(743\) | 34.0526 | 1.24927 | 0.624634 | − | 0.780918i | \(-0.285248\pi\) | ||||
0.624634 | + | 0.780918i | \(0.285248\pi\) | |||||||
\(744\) | −8.19615 | −0.300486 | ||||||||
\(745\) | 0.392305 | 0.0143729 | ||||||||
\(746\) | 6.07180 | 0.222304 | ||||||||
\(747\) | 11.3923 | 0.416823 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.7846 | 1.56332 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 27.8038 | 1.01458 | 0.507288 | − | 0.861776i | \(-0.330648\pi\) | ||||
0.507288 | + | 0.861776i | \(0.330648\pi\) | |||||||
\(752\) | 8.92820 | 0.325578 | ||||||||
\(753\) | 18.5359 | 0.675486 | ||||||||
\(754\) | 9.00000 | 0.327761 | ||||||||
\(755\) | −13.2679 | −0.482870 | ||||||||
\(756\) | −3.73205 | −0.135733 | ||||||||
\(757\) | −3.46410 | −0.125905 | −0.0629525 | − | 0.998017i | \(-0.520052\pi\) | ||||
−0.0629525 | + | 0.998017i | \(0.520052\pi\) | |||||||
\(758\) | −21.4449 | −0.778913 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.46410 | −0.161930 | ||||||||
\(761\) | −12.6795 | −0.459631 | −0.229816 | − | 0.973234i | \(-0.573812\pi\) | ||||
−0.229816 | + | 0.973234i | \(0.573812\pi\) | |||||||
\(762\) | −0.392305 | −0.0142117 | ||||||||
\(763\) | 50.2487 | 1.81913 | ||||||||
\(764\) | 18.4641 | 0.668008 | ||||||||
\(765\) | −0.267949 | −0.00968772 | ||||||||
\(766\) | 16.9282 | 0.611641 | ||||||||
\(767\) | 12.5885 | 0.454543 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −10.5167 | −0.379240 | −0.189620 | − | 0.981858i | \(-0.560726\pi\) | ||||
−0.189620 | + | 0.981858i | \(0.560726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.32051 | 0.227628 | ||||||||
\(772\) | −9.46410 | −0.340620 | ||||||||
\(773\) | 37.6603 | 1.35455 | 0.677273 | − | 0.735732i | \(-0.263162\pi\) | ||||
0.677273 | + | 0.735732i | \(0.263162\pi\) | |||||||
\(774\) | 6.73205 | 0.241979 | ||||||||
\(775\) | 8.19615 | 0.294414 | ||||||||
\(776\) | 18.7321 | 0.672441 | ||||||||
\(777\) | 6.46410 | 0.231898 | ||||||||
\(778\) | 37.8564 | 1.35722 | ||||||||
\(779\) | −21.1244 | −0.756859 | ||||||||
\(780\) | −3.00000 | −0.107417 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.26795 | −0.0453418 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 6.92820 | 0.247436 | ||||||||
\(785\) | 13.1962 | 0.470991 | ||||||||
\(786\) | 11.6603 | 0.415907 | ||||||||
\(787\) | −30.9808 | −1.10434 | −0.552172 | − | 0.833730i | \(-0.686201\pi\) | ||||
−0.552172 | + | 0.833730i | \(0.686201\pi\) | |||||||
\(788\) | 13.4641 | 0.479639 | ||||||||
\(789\) | 25.1244 | 0.894451 | ||||||||
\(790\) | 0.535898 | 0.0190664 | ||||||||
\(791\) | −51.7128 | −1.83870 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.58846 | −0.233963 | ||||||||
\(794\) | −25.9808 | −0.922023 | ||||||||
\(795\) | −5.26795 | −0.186835 | ||||||||
\(796\) | −16.3923 | −0.581010 | ||||||||
\(797\) | −25.3731 | −0.898760 | −0.449380 | − | 0.893341i | \(-0.648355\pi\) | ||||
−0.449380 | + | 0.893341i | \(0.648355\pi\) | |||||||
\(798\) | 16.6603 | 0.589767 | ||||||||
\(799\) | −2.39230 | −0.0846337 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −16.3923 | −0.579194 | ||||||||
\(802\) | −17.6603 | −0.623605 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.4641 | −0.404308 | ||||||||
\(805\) | 17.6603 | 0.622442 | ||||||||
\(806\) | 24.5885 | 0.866091 | ||||||||
\(807\) | 11.5885 | 0.407933 | ||||||||
\(808\) | −5.53590 | −0.194752 | ||||||||
\(809\) | 19.2679 | 0.677425 | 0.338713 | − | 0.940890i | \(-0.390009\pi\) | ||||
0.338713 | + | 0.940890i | \(0.390009\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 13.0000 | 0.456492 | 0.228246 | − | 0.973604i | \(-0.426701\pi\) | ||||
0.228246 | + | 0.973604i | \(0.426701\pi\) | |||||||
\(812\) | −11.1962 | −0.392908 | ||||||||
\(813\) | 23.8564 | 0.836681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.0526 | 0.632354 | ||||||||
\(816\) | −0.267949 | −0.00938010 | ||||||||
\(817\) | −30.0526 | −1.05141 | ||||||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 11.1962 | 0.391225 | ||||||||
\(820\) | −4.73205 | −0.165250 | ||||||||
\(821\) | 12.6795 | 0.442517 | 0.221259 | − | 0.975215i | \(-0.428983\pi\) | ||||
0.221259 | + | 0.975215i | \(0.428983\pi\) | |||||||
\(822\) | 19.7846 | 0.690068 | ||||||||
\(823\) | −19.3923 | −0.675973 | −0.337987 | − | 0.941151i | \(-0.609746\pi\) | ||||
−0.337987 | + | 0.941151i | \(0.609746\pi\) | |||||||
\(824\) | 18.3205 | 0.638225 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.6603 | −0.544890 | ||||||||
\(827\) | −54.5692 | −1.89756 | −0.948779 | − | 0.315941i | \(-0.897680\pi\) | ||||
−0.948779 | + | 0.315941i | \(0.897680\pi\) | |||||||
\(828\) | −4.73205 | −0.164450 | ||||||||
\(829\) | 12.8756 | 0.447190 | 0.223595 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223595 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(830\) | −11.3923 | −0.395433 | ||||||||
\(831\) | −18.9282 | −0.656612 | ||||||||
\(832\) | −3.00000 | −0.104006 | ||||||||
\(833\) | −1.85641 | −0.0643207 | ||||||||
\(834\) | 20.3205 | 0.703642 | ||||||||
\(835\) | 21.4641 | 0.742796 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.19615 | 0.283300 | ||||||||
\(838\) | 11.4641 | 0.396021 | ||||||||
\(839\) | 29.7846 | 1.02828 | 0.514139 | − | 0.857707i | \(-0.328111\pi\) | ||||
0.514139 | + | 0.857707i | \(0.328111\pi\) | |||||||
\(840\) | 3.73205 | 0.128768 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 4.05256 | 0.139660 | ||||||||
\(843\) | −26.0526 | −0.897298 | ||||||||
\(844\) | −17.7846 | −0.612172 | ||||||||
\(845\) | −4.00000 | −0.137604 | ||||||||
\(846\) | −8.92820 | −0.306958 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.26795 | −0.180902 | ||||||||
\(849\) | 30.2487 | 1.03813 | ||||||||
\(850\) | 0.267949 | 0.00919058 | ||||||||
\(851\) | 8.19615 | 0.280960 | ||||||||
\(852\) | −9.92820 | −0.340135 | ||||||||
\(853\) | −5.67949 | −0.194462 | −0.0972310 | − | 0.995262i | \(-0.530999\pi\) | ||||
−0.0972310 | + | 0.995262i | \(0.530999\pi\) | |||||||
\(854\) | 8.19615 | 0.280467 | ||||||||
\(855\) | 4.46410 | 0.152669 | ||||||||
\(856\) | 11.4641 | 0.391835 | ||||||||
\(857\) | 44.6603 | 1.52557 | 0.762783 | − | 0.646655i | \(-0.223833\pi\) | ||||
0.762783 | + | 0.646655i | \(0.223833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.60770 | −0.0548539 | −0.0274269 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274269 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(860\) | −6.73205 | −0.229561 | ||||||||
\(861\) | 17.6603 | 0.601860 | ||||||||
\(862\) | 6.12436 | 0.208596 | ||||||||
\(863\) | 12.2487 | 0.416951 | 0.208475 | − | 0.978028i | \(-0.433150\pi\) | ||||
0.208475 | + | 0.978028i | \(0.433150\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −14.5885 | −0.496022 | ||||||||
\(866\) | 10.9282 | 0.371355 | ||||||||
\(867\) | −16.9282 | −0.574912 | ||||||||
\(868\) | −30.5885 | −1.03824 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.00000 | −0.101710 | ||||||||
\(871\) | 34.3923 | 1.16534 | ||||||||
\(872\) | 13.4641 | 0.455952 | ||||||||
\(873\) | −18.7321 | −0.633984 | ||||||||
\(874\) | 21.1244 | 0.714542 | ||||||||
\(875\) | −3.73205 | −0.126166 | ||||||||
\(876\) | −6.19615 | −0.209349 | ||||||||
\(877\) | −33.6410 | −1.13598 | −0.567988 | − | 0.823037i | \(-0.692278\pi\) | ||||
−0.567988 | + | 0.823037i | \(0.692278\pi\) | |||||||
\(878\) | 4.92820 | 0.166319 | ||||||||
\(879\) | 18.9282 | 0.638432 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.4449 | 1.69953 | 0.849765 | − | 0.527161i | \(-0.176744\pi\) | ||||
0.849765 | + | 0.527161i | \(0.176744\pi\) | |||||||
\(882\) | −6.92820 | −0.233285 | ||||||||
\(883\) | 22.8756 | 0.769827 | 0.384913 | − | 0.922953i | \(-0.374231\pi\) | ||||
0.384913 | + | 0.922953i | \(0.374231\pi\) | |||||||
\(884\) | 0.803848 | 0.0270363 | ||||||||
\(885\) | −4.19615 | −0.141052 | ||||||||
\(886\) | 5.19615 | 0.174568 | ||||||||
\(887\) | −44.7846 | −1.50372 | −0.751860 | − | 0.659323i | \(-0.770843\pi\) | ||||
−0.751860 | + | 0.659323i | \(0.770843\pi\) | |||||||
\(888\) | 1.73205 | 0.0581238 | ||||||||
\(889\) | −1.46410 | −0.0491044 | ||||||||
\(890\) | 16.3923 | 0.549471 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.46410 | 0.216434 | ||||||||
\(893\) | 39.8564 | 1.33374 | ||||||||
\(894\) | −0.392305 | −0.0131206 | ||||||||
\(895\) | 7.12436 | 0.238141 | ||||||||
\(896\) | 3.73205 | 0.124679 | ||||||||
\(897\) | 14.1962 | 0.473996 | ||||||||
\(898\) | 3.46410 | 0.115599 | ||||||||
\(899\) | 24.5885 | 0.820071 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 1.41154 | 0.0470253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.1244 | 0.836086 | ||||||||
\(904\) | −13.8564 | −0.460857 | ||||||||
\(905\) | 4.19615 | 0.139485 | ||||||||
\(906\) | 13.2679 | 0.440798 | ||||||||
\(907\) | 13.2154 | 0.438810 | 0.219405 | − | 0.975634i | \(-0.429588\pi\) | ||||
0.219405 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(908\) | 10.3923 | 0.344881 | ||||||||
\(909\) | 5.53590 | 0.183614 | ||||||||
\(910\) | −11.1962 | −0.371149 | ||||||||
\(911\) | −30.5692 | −1.01280 | −0.506402 | − | 0.862298i | \(-0.669025\pi\) | ||||
−0.506402 | + | 0.862298i | \(0.669025\pi\) | |||||||
\(912\) | 4.46410 | 0.147821 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −30.4449 | −1.00703 | ||||||||
\(915\) | 2.19615 | 0.0726026 | ||||||||
\(916\) | −12.0000 | −0.396491 | ||||||||
\(917\) | 43.5167 | 1.43705 | ||||||||
\(918\) | 0.267949 | 0.00884364 | ||||||||
\(919\) | 14.3397 | 0.473025 | 0.236512 | − | 0.971628i | \(-0.423996\pi\) | ||||
0.236512 | + | 0.971628i | \(0.423996\pi\) | |||||||
\(920\) | 4.73205 | 0.156011 | ||||||||
\(921\) | −6.73205 | −0.221829 | ||||||||
\(922\) | −17.2487 | −0.568056 | ||||||||
\(923\) | 29.7846 | 0.980372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.73205 | −0.0569495 | ||||||||
\(926\) | 11.4641 | 0.376734 | ||||||||
\(927\) | −18.3205 | −0.601724 | ||||||||
\(928\) | −3.00000 | −0.0984798 | ||||||||
\(929\) | 9.12436 | 0.299360 | 0.149680 | − | 0.988734i | \(-0.452176\pi\) | ||||
0.149680 | + | 0.988734i | \(0.452176\pi\) | |||||||
\(930\) | −8.19615 | −0.268762 | ||||||||
\(931\) | 30.9282 | 1.01363 | ||||||||
\(932\) | −1.85641 | −0.0608086 | ||||||||
\(933\) | 13.8564 | 0.453638 | ||||||||
\(934\) | 30.1244 | 0.985699 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | 0.0980581 | ||||||||
\(937\) | 5.71281 | 0.186629 | 0.0933147 | − | 0.995637i | \(-0.470254\pi\) | ||||
0.0933147 | + | 0.995637i | \(0.470254\pi\) | |||||||
\(938\) | −42.7846 | −1.39697 | ||||||||
\(939\) | −19.1244 | −0.624100 | ||||||||
\(940\) | 8.92820 | 0.291206 | ||||||||
\(941\) | 19.9282 | 0.649641 | 0.324820 | − | 0.945776i | \(-0.394696\pi\) | ||||
0.324820 | + | 0.945776i | \(0.394696\pi\) | |||||||
\(942\) | −13.1962 | −0.429954 | ||||||||
\(943\) | 22.3923 | 0.729194 | ||||||||
\(944\) | −4.19615 | −0.136573 | ||||||||
\(945\) | −3.73205 | −0.121404 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.1962 | −0.948747 | −0.474374 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474374 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(948\) | −0.535898 | −0.0174052 | ||||||||
\(949\) | 18.5885 | 0.603407 | ||||||||
\(950\) | −4.46410 | −0.144835 | ||||||||
\(951\) | −15.1244 | −0.490441 | ||||||||
\(952\) | −1.00000 | −0.0324102 | ||||||||
\(953\) | 4.14359 | 0.134224 | 0.0671121 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671121 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(954\) | 5.26795 | 0.170556 | ||||||||
\(955\) | 18.4641 | 0.597484 | ||||||||
\(956\) | 6.26795 | 0.202720 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.26795 | −0.267125 | ||||||||
\(959\) | 73.8372 | 2.38433 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 36.1769 | 1.16700 | ||||||||
\(962\) | −5.19615 | −0.167531 | ||||||||
\(963\) | −11.4641 | −0.369426 | ||||||||
\(964\) | 22.6603 | 0.729838 | ||||||||
\(965\) | −9.46410 | −0.304660 | ||||||||
\(966\) | −17.6603 | −0.568209 | ||||||||
\(967\) | −35.4641 | −1.14045 | −0.570224 | − | 0.821489i | \(-0.693144\pi\) | ||||
−0.570224 | + | 0.821489i | \(0.693144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.19615 | −0.0384260 | ||||||||
\(970\) | 18.7321 | 0.601450 | ||||||||
\(971\) | −9.46410 | −0.303717 | −0.151859 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151859 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 75.8372 | 2.43123 | ||||||||
\(974\) | −6.46410 | −0.207123 | ||||||||
\(975\) | −3.00000 | −0.0960769 | ||||||||
\(976\) | 2.19615 | 0.0702971 | ||||||||
\(977\) | 10.0000 | 0.319928 | 0.159964 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159964 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(978\) | −18.0526 | −0.577257 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.92820 | 0.221313 | ||||||||
\(981\) | −13.4641 | −0.429876 | ||||||||
\(982\) | 1.26795 | 0.0404619 | ||||||||
\(983\) | 32.5885 | 1.03941 | 0.519705 | − | 0.854346i | \(-0.326042\pi\) | ||||
0.519705 | + | 0.854346i | \(0.326042\pi\) | |||||||
\(984\) | 4.73205 | 0.150852 | ||||||||
\(985\) | 13.4641 | 0.429002 | ||||||||
\(986\) | 0.803848 | 0.0255997 | ||||||||
\(987\) | −33.3205 | −1.06060 | ||||||||
\(988\) | −13.3923 | −0.426066 | ||||||||
\(989\) | 31.8564 | 1.01297 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.21539 | 0.292737 | 0.146368 | − | 0.989230i | \(-0.453242\pi\) | ||||
0.146368 | + | 0.989230i | \(0.453242\pi\) | |||||||
\(992\) | −8.19615 | −0.260228 | ||||||||
\(993\) | −30.5167 | −0.968417 | ||||||||
\(994\) | −37.0526 | −1.17524 | ||||||||
\(995\) | −16.3923 | −0.519671 | ||||||||
\(996\) | 11.3923 | 0.360979 | ||||||||
\(997\) | −59.3923 | −1.88097 | −0.940487 | − | 0.339831i | \(-0.889630\pi\) | ||||
−0.940487 | + | 0.339831i | \(0.889630\pi\) | |||||||
\(998\) | 21.4449 | 0.678825 | ||||||||
\(999\) | −1.73205 | −0.0547997 |
(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.bh.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 3630.2.a.bp.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3630.2.a.bh.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3630.2.a.bp.1.2 | yes | 2 | 11.10 | odd | 2 |