Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.19806 | 0.452825 | 0.226412 | − | 0.974032i | \(-0.427300\pi\) | ||||
0.226412 | + | 0.974032i | \(0.427300\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.93900 | −1.18765 | −0.593827 | − | 0.804593i | \(-0.702384\pi\) | ||||
−0.593827 | + | 0.804593i | \(0.702384\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.19806 | −0.320196 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.74094 | 0.422240 | 0.211120 | − | 0.977460i | \(-0.432289\pi\) | ||||
0.211120 | + | 0.977460i | \(0.432289\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.911854 | −0.209194 | −0.104597 | − | 0.994515i | \(-0.533355\pi\) | ||||
−0.104597 | + | 0.994515i | \(0.533355\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.19806 | −0.261439 | ||||||||
\(22\) | 3.93900 | 0.839798 | ||||||||
\(23\) | 1.24698 | 0.260013 | 0.130007 | − | 0.991513i | \(-0.458500\pi\) | ||||
0.130007 | + | 0.991513i | \(0.458500\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.19806 | 0.226412 | ||||||||
\(29\) | −3.47219 | −0.644769 | −0.322385 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322385 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 2.15883 | 0.387738 | 0.193869 | − | 0.981027i | \(-0.437896\pi\) | ||||
0.193869 | + | 0.981027i | \(0.437896\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.93900 | 0.685692 | ||||||||
\(34\) | −1.74094 | −0.298569 | ||||||||
\(35\) | 1.19806 | 0.202509 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.80194 | −0.789434 | −0.394717 | − | 0.918803i | \(-0.629157\pi\) | ||||
−0.394717 | + | 0.918803i | \(0.629157\pi\) | |||||||
\(38\) | 0.911854 | 0.147922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.198062 | −0.0309321 | −0.0154661 | − | 0.999880i | \(-0.504923\pi\) | ||||
−0.0154661 | + | 0.999880i | \(0.504923\pi\) | |||||||
\(42\) | 1.19806 | 0.184865 | ||||||||
\(43\) | 3.43296 | 0.523522 | 0.261761 | − | 0.965133i | \(-0.415697\pi\) | ||||
0.261761 | + | 0.965133i | \(0.415697\pi\) | |||||||
\(44\) | −3.93900 | −0.593827 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −1.24698 | −0.183857 | ||||||||
\(47\) | −0.902165 | −0.131594 | −0.0657972 | − | 0.997833i | \(-0.520959\pi\) | ||||
−0.0657972 | + | 0.997833i | \(0.520959\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.56465 | −0.794950 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.74094 | −0.243780 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.91185 | −0.949416 | −0.474708 | − | 0.880143i | \(-0.657446\pi\) | ||||
−0.474708 | + | 0.880143i | \(0.657446\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −3.93900 | −0.531135 | ||||||||
\(56\) | −1.19806 | −0.160098 | ||||||||
\(57\) | 0.911854 | 0.120778 | ||||||||
\(58\) | 3.47219 | 0.455921 | ||||||||
\(59\) | 10.2446 | 1.33373 | 0.666866 | − | 0.745178i | \(-0.267635\pi\) | ||||
0.666866 | + | 0.745178i | \(0.267635\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 9.92692 | 1.27101 | 0.635506 | − | 0.772096i | \(-0.280792\pi\) | ||||
0.635506 | + | 0.772096i | \(0.280792\pi\) | |||||||
\(62\) | −2.15883 | −0.274172 | ||||||||
\(63\) | 1.19806 | 0.150942 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.93900 | −0.484858 | ||||||||
\(67\) | 9.16852 | 1.12011 | 0.560057 | − | 0.828454i | \(-0.310779\pi\) | ||||
0.560057 | + | 0.828454i | \(0.310779\pi\) | |||||||
\(68\) | 1.74094 | 0.211120 | ||||||||
\(69\) | −1.24698 | −0.150119 | ||||||||
\(70\) | −1.19806 | −0.143196 | ||||||||
\(71\) | −11.0707 | −1.31385 | −0.656924 | − | 0.753956i | \(-0.728143\pi\) | ||||
−0.656924 | + | 0.753956i | \(0.728143\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −4.13706 | −0.484207 | −0.242103 | − | 0.970250i | \(-0.577837\pi\) | ||||
−0.242103 | + | 0.970250i | \(0.577837\pi\) | |||||||
\(74\) | 4.80194 | 0.558214 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −0.911854 | −0.104597 | ||||||||
\(77\) | −4.71917 | −0.537799 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.73556 | 0.307775 | 0.153887 | − | 0.988088i | \(-0.450821\pi\) | ||||
0.153887 | + | 0.988088i | \(0.450821\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.198062 | 0.0218723 | ||||||||
\(83\) | −15.5864 | −1.71083 | −0.855416 | − | 0.517942i | \(-0.826698\pi\) | ||||
−0.855416 | + | 0.517942i | \(0.826698\pi\) | |||||||
\(84\) | −1.19806 | −0.130719 | ||||||||
\(85\) | 1.74094 | 0.188831 | ||||||||
\(86\) | −3.43296 | −0.370186 | ||||||||
\(87\) | 3.47219 | 0.372258 | ||||||||
\(88\) | 3.93900 | 0.419899 | ||||||||
\(89\) | −8.57673 | −0.909131 | −0.454566 | − | 0.890713i | \(-0.650206\pi\) | ||||
−0.454566 | + | 0.890713i | \(0.650206\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.24698 | 0.130007 | ||||||||
\(93\) | −2.15883 | −0.223861 | ||||||||
\(94\) | 0.902165 | 0.0930512 | ||||||||
\(95\) | −0.911854 | −0.0935542 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.9976 | −1.72585 | −0.862923 | − | 0.505336i | \(-0.831369\pi\) | ||||
−0.862923 | + | 0.505336i | \(0.831369\pi\) | |||||||
\(98\) | 5.56465 | 0.562114 | ||||||||
\(99\) | −3.93900 | −0.395885 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.67025 | 0.663715 | 0.331857 | − | 0.943330i | \(-0.392325\pi\) | ||||
0.331857 | + | 0.943330i | \(0.392325\pi\) | |||||||
\(102\) | 1.74094 | 0.172379 | ||||||||
\(103\) | 10.0315 | 0.988429 | 0.494215 | − | 0.869340i | \(-0.335456\pi\) | ||||
0.494215 | + | 0.869340i | \(0.335456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.19806 | −0.116919 | ||||||||
\(106\) | 6.91185 | 0.671339 | ||||||||
\(107\) | −10.1032 | −0.976714 | −0.488357 | − | 0.872644i | \(-0.662404\pi\) | ||||
−0.488357 | + | 0.872644i | \(0.662404\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.5211 | −1.00774 | −0.503870 | − | 0.863780i | \(-0.668091\pi\) | ||||
−0.503870 | + | 0.863780i | \(0.668091\pi\) | |||||||
\(110\) | 3.93900 | 0.375569 | ||||||||
\(111\) | 4.80194 | 0.455780 | ||||||||
\(112\) | 1.19806 | 0.113206 | ||||||||
\(113\) | −11.2131 | −1.05484 | −0.527421 | − | 0.849604i | \(-0.676841\pi\) | ||||
−0.527421 | + | 0.849604i | \(0.676841\pi\) | |||||||
\(114\) | −0.911854 | −0.0854030 | ||||||||
\(115\) | 1.24698 | 0.116281 | ||||||||
\(116\) | −3.47219 | −0.322385 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.2446 | −0.943091 | ||||||||
\(119\) | 2.08575 | 0.191201 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 4.51573 | 0.410521 | ||||||||
\(122\) | −9.92692 | −0.898741 | ||||||||
\(123\) | 0.198062 | 0.0178587 | ||||||||
\(124\) | 2.15883 | 0.193869 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.19806 | −0.106732 | ||||||||
\(127\) | −9.32736 | −0.827669 | −0.413834 | − | 0.910352i | \(-0.635811\pi\) | ||||
−0.413834 | + | 0.910352i | \(0.635811\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.43296 | −0.302255 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.62133 | 0.403768 | 0.201884 | − | 0.979409i | \(-0.435294\pi\) | ||||
0.201884 | + | 0.979409i | \(0.435294\pi\) | |||||||
\(132\) | 3.93900 | 0.342846 | ||||||||
\(133\) | −1.09246 | −0.0947281 | ||||||||
\(134\) | −9.16852 | −0.792040 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.74094 | −0.149284 | ||||||||
\(137\) | −0.0760644 | −0.00649862 | −0.00324931 | − | 0.999995i | \(-0.501034\pi\) | ||||
−0.00324931 | + | 0.999995i | \(0.501034\pi\) | |||||||
\(138\) | 1.24698 | 0.106150 | ||||||||
\(139\) | 18.7017 | 1.58626 | 0.793129 | − | 0.609053i | \(-0.208451\pi\) | ||||
0.793129 | + | 0.609053i | \(0.208451\pi\) | |||||||
\(140\) | 1.19806 | 0.101255 | ||||||||
\(141\) | 0.902165 | 0.0759760 | ||||||||
\(142\) | 11.0707 | 0.929031 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.47219 | −0.288350 | ||||||||
\(146\) | 4.13706 | 0.342386 | ||||||||
\(147\) | 5.56465 | 0.458964 | ||||||||
\(148\) | −4.80194 | −0.394717 | ||||||||
\(149\) | −13.6799 | −1.12070 | −0.560352 | − | 0.828254i | \(-0.689334\pi\) | ||||
−0.560352 | + | 0.828254i | \(0.689334\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 1.15883 | 0.0943045 | 0.0471523 | − | 0.998888i | \(-0.484985\pi\) | ||||
0.0471523 | + | 0.998888i | \(0.484985\pi\) | |||||||
\(152\) | 0.911854 | 0.0739611 | ||||||||
\(153\) | 1.74094 | 0.140747 | ||||||||
\(154\) | 4.71917 | 0.380281 | ||||||||
\(155\) | 2.15883 | 0.173402 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2664 | −0.978962 | −0.489481 | − | 0.872014i | \(-0.662814\pi\) | ||||
−0.489481 | + | 0.872014i | \(0.662814\pi\) | |||||||
\(158\) | −2.73556 | −0.217630 | ||||||||
\(159\) | 6.91185 | 0.548146 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.49396 | 0.117740 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.48858 | 0.194921 | 0.0974604 | − | 0.995239i | \(-0.468928\pi\) | ||||
0.0974604 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(164\) | −0.198062 | −0.0154661 | ||||||||
\(165\) | 3.93900 | 0.306651 | ||||||||
\(166\) | 15.5864 | 1.20974 | ||||||||
\(167\) | −7.27950 | −0.563305 | −0.281652 | − | 0.959516i | \(-0.590883\pi\) | ||||
−0.281652 | + | 0.959516i | \(0.590883\pi\) | |||||||
\(168\) | 1.19806 | 0.0924325 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.74094 | −0.133524 | ||||||||
\(171\) | −0.911854 | −0.0697312 | ||||||||
\(172\) | 3.43296 | 0.261761 | ||||||||
\(173\) | 15.8485 | 1.20494 | 0.602468 | − | 0.798143i | \(-0.294184\pi\) | ||||
0.602468 | + | 0.798143i | \(0.294184\pi\) | |||||||
\(174\) | −3.47219 | −0.263226 | ||||||||
\(175\) | 1.19806 | 0.0905650 | ||||||||
\(176\) | −3.93900 | −0.296913 | ||||||||
\(177\) | −10.2446 | −0.770030 | ||||||||
\(178\) | 8.57673 | 0.642853 | ||||||||
\(179\) | 18.4819 | 1.38140 | 0.690700 | − | 0.723141i | \(-0.257302\pi\) | ||||
0.690700 | + | 0.723141i | \(0.257302\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 10.7041 | 0.795630 | 0.397815 | − | 0.917466i | \(-0.369769\pi\) | ||||
0.397815 | + | 0.917466i | \(0.369769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.92692 | −0.733819 | ||||||||
\(184\) | −1.24698 | −0.0919286 | ||||||||
\(185\) | −4.80194 | −0.353045 | ||||||||
\(186\) | 2.15883 | 0.158293 | ||||||||
\(187\) | −6.85756 | −0.501474 | ||||||||
\(188\) | −0.902165 | −0.0657972 | ||||||||
\(189\) | −1.19806 | −0.0871462 | ||||||||
\(190\) | 0.911854 | 0.0661528 | ||||||||
\(191\) | 15.3623 | 1.11158 | 0.555788 | − | 0.831324i | \(-0.312417\pi\) | ||||
0.555788 | + | 0.831324i | \(0.312417\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 18.3207 | 1.31875 | 0.659375 | − | 0.751815i | \(-0.270821\pi\) | ||||
0.659375 | + | 0.751815i | \(0.270821\pi\) | |||||||
\(194\) | 16.9976 | 1.22036 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.56465 | −0.397475 | ||||||||
\(197\) | 2.31336 | 0.164820 | 0.0824099 | − | 0.996599i | \(-0.473738\pi\) | ||||
0.0824099 | + | 0.996599i | \(0.473738\pi\) | |||||||
\(198\) | 3.93900 | 0.279933 | ||||||||
\(199\) | 6.36765 | 0.451391 | 0.225695 | − | 0.974198i | \(-0.427535\pi\) | ||||
0.225695 | + | 0.974198i | \(0.427535\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −9.16852 | −0.646698 | ||||||||
\(202\) | −6.67025 | −0.469317 | ||||||||
\(203\) | −4.15990 | −0.291968 | ||||||||
\(204\) | −1.74094 | −0.121890 | ||||||||
\(205\) | −0.198062 | −0.0138333 | ||||||||
\(206\) | −10.0315 | −0.698925 | ||||||||
\(207\) | 1.24698 | 0.0866711 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.59179 | 0.248450 | ||||||||
\(210\) | 1.19806 | 0.0826742 | ||||||||
\(211\) | −11.6775 | −0.803915 | −0.401958 | − | 0.915658i | \(-0.631670\pi\) | ||||
−0.401958 | + | 0.915658i | \(0.631670\pi\) | |||||||
\(212\) | −6.91185 | −0.474708 | ||||||||
\(213\) | 11.0707 | 0.758551 | ||||||||
\(214\) | 10.1032 | 0.690641 | ||||||||
\(215\) | 3.43296 | 0.234126 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.58642 | 0.175577 | ||||||||
\(218\) | 10.5211 | 0.712579 | ||||||||
\(219\) | 4.13706 | 0.279557 | ||||||||
\(220\) | −3.93900 | −0.265567 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.80194 | −0.322285 | ||||||||
\(223\) | −11.4004 | −0.763430 | −0.381715 | − | 0.924280i | \(-0.624666\pi\) | ||||
−0.381715 | + | 0.924280i | \(0.624666\pi\) | |||||||
\(224\) | −1.19806 | −0.0800489 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 11.2131 | 0.745886 | ||||||||
\(227\) | −8.86725 | −0.588540 | −0.294270 | − | 0.955722i | \(-0.595076\pi\) | ||||
−0.294270 | + | 0.955722i | \(0.595076\pi\) | |||||||
\(228\) | 0.911854 | 0.0603890 | ||||||||
\(229\) | −12.6136 | −0.833528 | −0.416764 | − | 0.909015i | \(-0.636836\pi\) | ||||
−0.416764 | + | 0.909015i | \(0.636836\pi\) | |||||||
\(230\) | −1.24698 | −0.0822234 | ||||||||
\(231\) | 4.71917 | 0.310498 | ||||||||
\(232\) | 3.47219 | 0.227960 | ||||||||
\(233\) | −23.4155 | −1.53400 | −0.767000 | − | 0.641647i | \(-0.778252\pi\) | ||||
−0.767000 | + | 0.641647i | \(0.778252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.902165 | −0.0588508 | ||||||||
\(236\) | 10.2446 | 0.666866 | ||||||||
\(237\) | −2.73556 | −0.177694 | ||||||||
\(238\) | −2.08575 | −0.135199 | ||||||||
\(239\) | −8.87263 | −0.573922 | −0.286961 | − | 0.957942i | \(-0.592645\pi\) | ||||
−0.286961 | + | 0.957942i | \(0.592645\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −9.72886 | −0.626691 | −0.313345 | − | 0.949639i | \(-0.601450\pi\) | ||||
−0.313345 | + | 0.949639i | \(0.601450\pi\) | |||||||
\(242\) | −4.51573 | −0.290282 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.92692 | 0.635506 | ||||||||
\(245\) | −5.56465 | −0.355512 | ||||||||
\(246\) | −0.198062 | −0.0126280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.15883 | −0.137086 | ||||||||
\(249\) | 15.5864 | 0.987749 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 29.8823 | 1.88615 | 0.943077 | − | 0.332573i | \(-0.107917\pi\) | ||||
0.943077 | + | 0.332573i | \(0.107917\pi\) | |||||||
\(252\) | 1.19806 | 0.0754708 | ||||||||
\(253\) | −4.91185 | −0.308806 | ||||||||
\(254\) | 9.32736 | 0.585250 | ||||||||
\(255\) | −1.74094 | −0.109022 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.52111 | −0.531532 | −0.265766 | − | 0.964038i | \(-0.585625\pi\) | ||||
−0.265766 | + | 0.964038i | \(0.585625\pi\) | |||||||
\(258\) | 3.43296 | 0.213727 | ||||||||
\(259\) | −5.75302 | −0.357475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.47219 | −0.214923 | ||||||||
\(262\) | −4.62133 | −0.285507 | ||||||||
\(263\) | −22.6450 | −1.39635 | −0.698176 | − | 0.715926i | \(-0.746005\pi\) | ||||
−0.698176 | + | 0.715926i | \(0.746005\pi\) | |||||||
\(264\) | −3.93900 | −0.242429 | ||||||||
\(265\) | −6.91185 | −0.424592 | ||||||||
\(266\) | 1.09246 | 0.0669829 | ||||||||
\(267\) | 8.57673 | 0.524887 | ||||||||
\(268\) | 9.16852 | 0.560057 | ||||||||
\(269\) | −9.02608 | −0.550330 | −0.275165 | − | 0.961397i | \(-0.588732\pi\) | ||||
−0.275165 | + | 0.961397i | \(0.588732\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 8.59611 | 0.522176 | 0.261088 | − | 0.965315i | \(-0.415919\pi\) | ||||
0.261088 | + | 0.965315i | \(0.415919\pi\) | |||||||
\(272\) | 1.74094 | 0.105560 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0760644 | 0.00459522 | ||||||||
\(275\) | −3.93900 | −0.237531 | ||||||||
\(276\) | −1.24698 | −0.0750594 | ||||||||
\(277\) | 6.31527 | 0.379448 | 0.189724 | − | 0.981837i | \(-0.439241\pi\) | ||||
0.189724 | + | 0.981837i | \(0.439241\pi\) | |||||||
\(278\) | −18.7017 | −1.12165 | ||||||||
\(279\) | 2.15883 | 0.129246 | ||||||||
\(280\) | −1.19806 | −0.0715979 | ||||||||
\(281\) | −21.7409 | −1.29696 | −0.648478 | − | 0.761234i | \(-0.724594\pi\) | ||||
−0.648478 | + | 0.761234i | \(0.724594\pi\) | |||||||
\(282\) | −0.902165 | −0.0537232 | ||||||||
\(283\) | 12.9487 | 0.769720 | 0.384860 | − | 0.922975i | \(-0.374250\pi\) | ||||
0.384860 | + | 0.922975i | \(0.374250\pi\) | |||||||
\(284\) | −11.0707 | −0.656924 | ||||||||
\(285\) | 0.911854 | 0.0540136 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.237291 | −0.0140068 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −13.9691 | −0.821714 | ||||||||
\(290\) | 3.47219 | 0.203894 | ||||||||
\(291\) | 16.9976 | 0.996417 | ||||||||
\(292\) | −4.13706 | −0.242103 | ||||||||
\(293\) | −27.3056 | −1.59521 | −0.797605 | − | 0.603181i | \(-0.793900\pi\) | ||||
−0.797605 | + | 0.603181i | \(0.793900\pi\) | |||||||
\(294\) | −5.56465 | −0.324537 | ||||||||
\(295\) | 10.2446 | 0.596463 | ||||||||
\(296\) | 4.80194 | 0.279107 | ||||||||
\(297\) | 3.93900 | 0.228564 | ||||||||
\(298\) | 13.6799 | 0.792458 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 4.11290 | 0.237064 | ||||||||
\(302\) | −1.15883 | −0.0666834 | ||||||||
\(303\) | −6.67025 | −0.383196 | ||||||||
\(304\) | −0.911854 | −0.0522984 | ||||||||
\(305\) | 9.92692 | 0.568414 | ||||||||
\(306\) | −1.74094 | −0.0995228 | ||||||||
\(307\) | 24.9124 | 1.42183 | 0.710914 | − | 0.703279i | \(-0.248281\pi\) | ||||
0.710914 | + | 0.703279i | \(0.248281\pi\) | |||||||
\(308\) | −4.71917 | −0.268900 | ||||||||
\(309\) | −10.0315 | −0.570670 | ||||||||
\(310\) | −2.15883 | −0.122614 | ||||||||
\(311\) | 21.3787 | 1.21227 | 0.606136 | − | 0.795361i | \(-0.292719\pi\) | ||||
0.606136 | + | 0.795361i | \(0.292719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8713 | −1.34929 | −0.674643 | − | 0.738144i | \(-0.735702\pi\) | ||||
−0.674643 | + | 0.738144i | \(0.735702\pi\) | |||||||
\(314\) | 12.2664 | 0.692231 | ||||||||
\(315\) | 1.19806 | 0.0675032 | ||||||||
\(316\) | 2.73556 | 0.153887 | ||||||||
\(317\) | 12.6407 | 0.709973 | 0.354987 | − | 0.934871i | \(-0.384485\pi\) | ||||
0.354987 | + | 0.934871i | \(0.384485\pi\) | |||||||
\(318\) | −6.91185 | −0.387598 | ||||||||
\(319\) | 13.6770 | 0.765763 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 10.1032 | 0.563906 | ||||||||
\(322\) | −1.49396 | −0.0832551 | ||||||||
\(323\) | −1.58748 | −0.0883299 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.48858 | −0.137830 | ||||||||
\(327\) | 10.5211 | 0.581819 | ||||||||
\(328\) | 0.198062 | 0.0109362 | ||||||||
\(329\) | −1.08085 | −0.0595892 | ||||||||
\(330\) | −3.93900 | −0.216835 | ||||||||
\(331\) | −20.5109 | −1.12738 | −0.563692 | − | 0.825985i | \(-0.690619\pi\) | ||||
−0.563692 | + | 0.825985i | \(0.690619\pi\) | |||||||
\(332\) | −15.5864 | −0.855416 | ||||||||
\(333\) | −4.80194 | −0.263145 | ||||||||
\(334\) | 7.27950 | 0.398317 | ||||||||
\(335\) | 9.16852 | 0.500930 | ||||||||
\(336\) | −1.19806 | −0.0653597 | ||||||||
\(337\) | 6.82371 | 0.371711 | 0.185856 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185856 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2131 | 0.609014 | ||||||||
\(340\) | 1.74094 | 0.0944157 | ||||||||
\(341\) | −8.50365 | −0.460498 | ||||||||
\(342\) | 0.911854 | 0.0493074 | ||||||||
\(343\) | −15.0532 | −0.812798 | ||||||||
\(344\) | −3.43296 | −0.185093 | ||||||||
\(345\) | −1.24698 | −0.0671351 | ||||||||
\(346\) | −15.8485 | −0.852019 | ||||||||
\(347\) | −29.4741 | −1.58225 | −0.791127 | − | 0.611653i | \(-0.790505\pi\) | ||||
−0.791127 | + | 0.611653i | \(0.790505\pi\) | |||||||
\(348\) | 3.47219 | 0.186129 | ||||||||
\(349\) | 34.5394 | 1.84885 | 0.924426 | − | 0.381361i | \(-0.124544\pi\) | ||||
0.924426 | + | 0.381361i | \(0.124544\pi\) | |||||||
\(350\) | −1.19806 | −0.0640391 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.93900 | 0.209949 | ||||||||
\(353\) | −31.2295 | −1.66218 | −0.831090 | − | 0.556138i | \(-0.812283\pi\) | ||||
−0.831090 | + | 0.556138i | \(0.812283\pi\) | |||||||
\(354\) | 10.2446 | 0.544494 | ||||||||
\(355\) | −11.0707 | −0.587571 | ||||||||
\(356\) | −8.57673 | −0.454566 | ||||||||
\(357\) | −2.08575 | −0.110390 | ||||||||
\(358\) | −18.4819 | −0.976798 | ||||||||
\(359\) | −18.2524 | −0.963323 | −0.481661 | − | 0.876357i | \(-0.659966\pi\) | ||||
−0.481661 | + | 0.876357i | \(0.659966\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −18.1685 | −0.956238 | ||||||||
\(362\) | −10.7041 | −0.562595 | ||||||||
\(363\) | −4.51573 | −0.237014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.13706 | −0.216544 | ||||||||
\(366\) | 9.92692 | 0.518888 | ||||||||
\(367\) | −19.3773 | −1.01149 | −0.505744 | − | 0.862683i | \(-0.668782\pi\) | ||||
−0.505744 | + | 0.862683i | \(0.668782\pi\) | |||||||
\(368\) | 1.24698 | 0.0650033 | ||||||||
\(369\) | −0.198062 | −0.0103107 | ||||||||
\(370\) | 4.80194 | 0.249641 | ||||||||
\(371\) | −8.28083 | −0.429919 | ||||||||
\(372\) | −2.15883 | −0.111930 | ||||||||
\(373\) | −13.6280 | −0.705633 | −0.352817 | − | 0.935693i | \(-0.614776\pi\) | ||||
−0.352817 | + | 0.935693i | \(0.614776\pi\) | |||||||
\(374\) | 6.85756 | 0.354596 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0.902165 | 0.0465256 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.19806 | 0.0616217 | ||||||||
\(379\) | 1.32006 | 0.0678069 | 0.0339035 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339035 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(380\) | −0.911854 | −0.0467771 | ||||||||
\(381\) | 9.32736 | 0.477855 | ||||||||
\(382\) | −15.3623 | −0.786002 | ||||||||
\(383\) | −25.5308 | −1.30456 | −0.652281 | − | 0.757977i | \(-0.726188\pi\) | ||||
−0.652281 | + | 0.757977i | \(0.726188\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −4.71917 | −0.240511 | ||||||||
\(386\) | −18.3207 | −0.932497 | ||||||||
\(387\) | 3.43296 | 0.174507 | ||||||||
\(388\) | −16.9976 | −0.862923 | ||||||||
\(389\) | −6.05967 | −0.307238 | −0.153619 | − | 0.988130i | \(-0.549093\pi\) | ||||
−0.153619 | + | 0.988130i | \(0.549093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17092 | 0.109788 | ||||||||
\(392\) | 5.56465 | 0.281057 | ||||||||
\(393\) | −4.62133 | −0.233115 | ||||||||
\(394\) | −2.31336 | −0.116545 | ||||||||
\(395\) | 2.73556 | 0.137641 | ||||||||
\(396\) | −3.93900 | −0.197942 | ||||||||
\(397\) | −5.99330 | −0.300795 | −0.150397 | − | 0.988626i | \(-0.548055\pi\) | ||||
−0.150397 | + | 0.988626i | \(0.548055\pi\) | |||||||
\(398\) | −6.36765 | −0.319181 | ||||||||
\(399\) | 1.09246 | 0.0546913 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −17.3773 | −0.867783 | −0.433891 | − | 0.900965i | \(-0.642860\pi\) | ||||
−0.433891 | + | 0.900965i | \(0.642860\pi\) | |||||||
\(402\) | 9.16852 | 0.457284 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.67025 | 0.331857 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 4.15990 | 0.206452 | ||||||||
\(407\) | 18.9148 | 0.937574 | ||||||||
\(408\) | 1.74094 | 0.0861893 | ||||||||
\(409\) | −29.3672 | −1.45211 | −0.726057 | − | 0.687635i | \(-0.758649\pi\) | ||||
−0.726057 | + | 0.687635i | \(0.758649\pi\) | |||||||
\(410\) | 0.198062 | 0.00978160 | ||||||||
\(411\) | 0.0760644 | 0.00375198 | ||||||||
\(412\) | 10.0315 | 0.494215 | ||||||||
\(413\) | 12.2737 | 0.603947 | ||||||||
\(414\) | −1.24698 | −0.0612857 | ||||||||
\(415\) | −15.5864 | −0.765107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7017 | −0.915827 | ||||||||
\(418\) | −3.59179 | −0.175680 | ||||||||
\(419\) | −26.5472 | −1.29692 | −0.648458 | − | 0.761251i | \(-0.724586\pi\) | ||||
−0.648458 | + | 0.761251i | \(0.724586\pi\) | |||||||
\(420\) | −1.19806 | −0.0584595 | ||||||||
\(421\) | 31.0834 | 1.51491 | 0.757455 | − | 0.652887i | \(-0.226442\pi\) | ||||
0.757455 | + | 0.652887i | \(0.226442\pi\) | |||||||
\(422\) | 11.6775 | 0.568454 | ||||||||
\(423\) | −0.902165 | −0.0438648 | ||||||||
\(424\) | 6.91185 | 0.335669 | ||||||||
\(425\) | 1.74094 | 0.0844479 | ||||||||
\(426\) | −11.0707 | −0.536377 | ||||||||
\(427\) | 11.8931 | 0.575546 | ||||||||
\(428\) | −10.1032 | −0.488357 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.43296 | −0.165552 | ||||||||
\(431\) | −36.1226 | −1.73996 | −0.869982 | − | 0.493084i | \(-0.835870\pi\) | ||||
−0.869982 | + | 0.493084i | \(0.835870\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −35.2868 | −1.69578 | −0.847888 | − | 0.530176i | \(-0.822126\pi\) | ||||
−0.847888 | + | 0.530176i | \(0.822126\pi\) | |||||||
\(434\) | −2.58642 | −0.124152 | ||||||||
\(435\) | 3.47219 | 0.166479 | ||||||||
\(436\) | −10.5211 | −0.503870 | ||||||||
\(437\) | −1.13706 | −0.0543931 | ||||||||
\(438\) | −4.13706 | −0.197677 | ||||||||
\(439\) | −32.0170 | −1.52809 | −0.764044 | − | 0.645165i | \(-0.776789\pi\) | ||||
−0.764044 | + | 0.645165i | \(0.776789\pi\) | |||||||
\(440\) | 3.93900 | 0.187785 | ||||||||
\(441\) | −5.56465 | −0.264983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5948 | −1.12102 | −0.560511 | − | 0.828147i | \(-0.689395\pi\) | ||||
−0.560511 | + | 0.828147i | \(0.689395\pi\) | |||||||
\(444\) | 4.80194 | 0.227890 | ||||||||
\(445\) | −8.57673 | −0.406576 | ||||||||
\(446\) | 11.4004 | 0.539826 | ||||||||
\(447\) | 13.6799 | 0.647039 | ||||||||
\(448\) | 1.19806 | 0.0566031 | ||||||||
\(449\) | 19.8374 | 0.936187 | 0.468093 | − | 0.883679i | \(-0.344941\pi\) | ||||
0.468093 | + | 0.883679i | \(0.344941\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0.780167 | 0.0367367 | ||||||||
\(452\) | −11.2131 | −0.527421 | ||||||||
\(453\) | −1.15883 | −0.0544468 | ||||||||
\(454\) | 8.86725 | 0.416161 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.911854 | −0.0427015 | ||||||||
\(457\) | 26.5284 | 1.24095 | 0.620473 | − | 0.784228i | \(-0.286941\pi\) | ||||
0.620473 | + | 0.784228i | \(0.286941\pi\) | |||||||
\(458\) | 12.6136 | 0.589393 | ||||||||
\(459\) | −1.74094 | −0.0812601 | ||||||||
\(460\) | 1.24698 | 0.0581407 | ||||||||
\(461\) | 12.2717 | 0.571552 | 0.285776 | − | 0.958297i | \(-0.407749\pi\) | ||||
0.285776 | + | 0.958297i | \(0.407749\pi\) | |||||||
\(462\) | −4.71917 | −0.219556 | ||||||||
\(463\) | 12.6455 | 0.587686 | 0.293843 | − | 0.955854i | \(-0.405066\pi\) | ||||
0.293843 | + | 0.955854i | \(0.405066\pi\) | |||||||
\(464\) | −3.47219 | −0.161192 | ||||||||
\(465\) | −2.15883 | −0.100114 | ||||||||
\(466\) | 23.4155 | 1.08470 | ||||||||
\(467\) | 11.3870 | 0.526929 | 0.263464 | − | 0.964669i | \(-0.415135\pi\) | ||||
0.263464 | + | 0.964669i | \(0.415135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9845 | 0.507215 | ||||||||
\(470\) | 0.902165 | 0.0416138 | ||||||||
\(471\) | 12.2664 | 0.565204 | ||||||||
\(472\) | −10.2446 | −0.471545 | ||||||||
\(473\) | −13.5224 | −0.621762 | ||||||||
\(474\) | 2.73556 | 0.125649 | ||||||||
\(475\) | −0.911854 | −0.0418387 | ||||||||
\(476\) | 2.08575 | 0.0956003 | ||||||||
\(477\) | −6.91185 | −0.316472 | ||||||||
\(478\) | 8.87263 | 0.405824 | ||||||||
\(479\) | −18.8431 | −0.860963 | −0.430481 | − | 0.902600i | \(-0.641656\pi\) | ||||
−0.430481 | + | 0.902600i | \(0.641656\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 9.72886 | 0.443137 | ||||||||
\(483\) | −1.49396 | −0.0679775 | ||||||||
\(484\) | 4.51573 | 0.205260 | ||||||||
\(485\) | −16.9976 | −0.771822 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −27.6383 | −1.25241 | −0.626206 | − | 0.779658i | \(-0.715393\pi\) | ||||
−0.626206 | + | 0.779658i | \(0.715393\pi\) | |||||||
\(488\) | −9.92692 | −0.449371 | ||||||||
\(489\) | −2.48858 | −0.112538 | ||||||||
\(490\) | 5.56465 | 0.251385 | ||||||||
\(491\) | −13.9866 | −0.631206 | −0.315603 | − | 0.948891i | \(-0.602207\pi\) | ||||
−0.315603 | + | 0.948891i | \(0.602207\pi\) | |||||||
\(492\) | 0.198062 | 0.00892934 | ||||||||
\(493\) | −6.04487 | −0.272247 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.93900 | −0.177045 | ||||||||
\(496\) | 2.15883 | 0.0969345 | ||||||||
\(497\) | −13.2634 | −0.594944 | ||||||||
\(498\) | −15.5864 | −0.698444 | ||||||||
\(499\) | 8.87071 | 0.397107 | 0.198554 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198554 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 7.27950 | 0.325224 | ||||||||
\(502\) | −29.8823 | −1.33371 | ||||||||
\(503\) | 1.99761 | 0.0890689 | 0.0445344 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445344 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(504\) | −1.19806 | −0.0533659 | ||||||||
\(505\) | 6.67025 | 0.296822 | ||||||||
\(506\) | 4.91185 | 0.218359 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.32736 | −0.413834 | ||||||||
\(509\) | 21.7023 | 0.961938 | 0.480969 | − | 0.876738i | \(-0.340285\pi\) | ||||
0.480969 | + | 0.876738i | \(0.340285\pi\) | |||||||
\(510\) | 1.74094 | 0.0770901 | ||||||||
\(511\) | −4.95646 | −0.219261 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.911854 | 0.0402593 | ||||||||
\(514\) | 8.52111 | 0.375850 | ||||||||
\(515\) | 10.0315 | 0.442039 | ||||||||
\(516\) | −3.43296 | −0.151128 | ||||||||
\(517\) | 3.55363 | 0.156288 | ||||||||
\(518\) | 5.75302 | 0.252773 | ||||||||
\(519\) | −15.8485 | −0.695670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8364 | 0.518561 | 0.259281 | − | 0.965802i | \(-0.416515\pi\) | ||||
0.259281 | + | 0.965802i | \(0.416515\pi\) | |||||||
\(522\) | 3.47219 | 0.151974 | ||||||||
\(523\) | 24.6112 | 1.07617 | 0.538086 | − | 0.842890i | \(-0.319148\pi\) | ||||
0.538086 | + | 0.842890i | \(0.319148\pi\) | |||||||
\(524\) | 4.62133 | 0.201884 | ||||||||
\(525\) | −1.19806 | −0.0522877 | ||||||||
\(526\) | 22.6450 | 0.987370 | ||||||||
\(527\) | 3.75840 | 0.163718 | ||||||||
\(528\) | 3.93900 | 0.171423 | ||||||||
\(529\) | −21.4450 | −0.932393 | ||||||||
\(530\) | 6.91185 | 0.300232 | ||||||||
\(531\) | 10.2446 | 0.444577 | ||||||||
\(532\) | −1.09246 | −0.0473641 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.57673 | −0.371151 | ||||||||
\(535\) | −10.1032 | −0.436800 | ||||||||
\(536\) | −9.16852 | −0.396020 | ||||||||
\(537\) | −18.4819 | −0.797552 | ||||||||
\(538\) | 9.02608 | 0.389142 | ||||||||
\(539\) | 21.9191 | 0.944125 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −29.1282 | −1.25232 | −0.626160 | − | 0.779694i | \(-0.715374\pi\) | ||||
−0.626160 | + | 0.779694i | \(0.715374\pi\) | |||||||
\(542\) | −8.59611 | −0.369234 | ||||||||
\(543\) | −10.7041 | −0.459357 | ||||||||
\(544\) | −1.74094 | −0.0746421 | ||||||||
\(545\) | −10.5211 | −0.450675 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.1752 | −0.435061 | −0.217531 | − | 0.976053i | \(-0.569800\pi\) | ||||
−0.217531 | + | 0.976053i | \(0.569800\pi\) | |||||||
\(548\) | −0.0760644 | −0.00324931 | ||||||||
\(549\) | 9.92692 | 0.423671 | ||||||||
\(550\) | 3.93900 | 0.167960 | ||||||||
\(551\) | 3.16613 | 0.134882 | ||||||||
\(552\) | 1.24698 | 0.0530750 | ||||||||
\(553\) | 3.27737 | 0.139368 | ||||||||
\(554\) | −6.31527 | −0.268310 | ||||||||
\(555\) | 4.80194 | 0.203831 | ||||||||
\(556\) | 18.7017 | 0.793129 | ||||||||
\(557\) | −13.0398 | −0.552515 | −0.276257 | − | 0.961084i | \(-0.589094\pi\) | ||||
−0.276257 | + | 0.961084i | \(0.589094\pi\) | |||||||
\(558\) | −2.15883 | −0.0913907 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.19806 | 0.0506274 | ||||||||
\(561\) | 6.85756 | 0.289526 | ||||||||
\(562\) | 21.7409 | 0.917086 | ||||||||
\(563\) | −32.9221 | −1.38750 | −0.693751 | − | 0.720215i | \(-0.744043\pi\) | ||||
−0.693751 | + | 0.720215i | \(0.744043\pi\) | |||||||
\(564\) | 0.902165 | 0.0379880 | ||||||||
\(565\) | −11.2131 | −0.471740 | ||||||||
\(566\) | −12.9487 | −0.544274 | ||||||||
\(567\) | 1.19806 | 0.0503139 | ||||||||
\(568\) | 11.0707 | 0.464516 | ||||||||
\(569\) | 7.53319 | 0.315808 | 0.157904 | − | 0.987454i | \(-0.449526\pi\) | ||||
0.157904 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(570\) | −0.911854 | −0.0381934 | ||||||||
\(571\) | 36.2422 | 1.51669 | 0.758344 | − | 0.651854i | \(-0.226009\pi\) | ||||
0.758344 | + | 0.651854i | \(0.226009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3623 | −0.641768 | ||||||||
\(574\) | 0.237291 | 0.00990433 | ||||||||
\(575\) | 1.24698 | 0.0520026 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.2198 | 0.591979 | 0.295990 | − | 0.955191i | \(-0.404351\pi\) | ||||
0.295990 | + | 0.955191i | \(0.404351\pi\) | |||||||
\(578\) | 13.9691 | 0.581039 | ||||||||
\(579\) | −18.3207 | −0.761380 | ||||||||
\(580\) | −3.47219 | −0.144175 | ||||||||
\(581\) | −18.6735 | −0.774707 | ||||||||
\(582\) | −16.9976 | −0.704573 | ||||||||
\(583\) | 27.2258 | 1.12758 | ||||||||
\(584\) | 4.13706 | 0.171193 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.3056 | 1.12798 | ||||||||
\(587\) | −22.3207 | −0.921272 | −0.460636 | − | 0.887589i | \(-0.652379\pi\) | ||||
−0.460636 | + | 0.887589i | \(0.652379\pi\) | |||||||
\(588\) | 5.56465 | 0.229482 | ||||||||
\(589\) | −1.96854 | −0.0811123 | ||||||||
\(590\) | −10.2446 | −0.421763 | ||||||||
\(591\) | −2.31336 | −0.0951587 | ||||||||
\(592\) | −4.80194 | −0.197358 | ||||||||
\(593\) | 1.64742 | 0.0676513 | 0.0338256 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338256 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(594\) | −3.93900 | −0.161619 | ||||||||
\(595\) | 2.08575 | 0.0855075 | ||||||||
\(596\) | −13.6799 | −0.560352 | ||||||||
\(597\) | −6.36765 | −0.260611 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.41119 | 0.384531 | 0.192265 | − | 0.981343i | \(-0.438417\pi\) | ||||
0.192265 | + | 0.981343i | \(0.438417\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 1.62565 | 0.0663115 | 0.0331557 | − | 0.999450i | \(-0.489444\pi\) | ||||
0.0331557 | + | 0.999450i | \(0.489444\pi\) | |||||||
\(602\) | −4.11290 | −0.167629 | ||||||||
\(603\) | 9.16852 | 0.373371 | ||||||||
\(604\) | 1.15883 | 0.0471523 | ||||||||
\(605\) | 4.51573 | 0.183591 | ||||||||
\(606\) | 6.67025 | 0.270960 | ||||||||
\(607\) | 14.9282 | 0.605919 | 0.302959 | − | 0.953003i | \(-0.402025\pi\) | ||||
0.302959 | + | 0.953003i | \(0.402025\pi\) | |||||||
\(608\) | 0.911854 | 0.0369806 | ||||||||
\(609\) | 4.15990 | 0.168568 | ||||||||
\(610\) | −9.92692 | −0.401929 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.74094 | 0.0703733 | ||||||||
\(613\) | −28.8437 | −1.16499 | −0.582493 | − | 0.812836i | \(-0.697922\pi\) | ||||
−0.582493 | + | 0.812836i | \(0.697922\pi\) | |||||||
\(614\) | −24.9124 | −1.00538 | ||||||||
\(615\) | 0.198062 | 0.00798664 | ||||||||
\(616\) | 4.71917 | 0.190141 | ||||||||
\(617\) | 39.7985 | 1.60223 | 0.801113 | − | 0.598513i | \(-0.204241\pi\) | ||||
0.801113 | + | 0.598513i | \(0.204241\pi\) | |||||||
\(618\) | 10.0315 | 0.403524 | ||||||||
\(619\) | 38.0465 | 1.52922 | 0.764609 | − | 0.644494i | \(-0.222932\pi\) | ||||
0.764609 | + | 0.644494i | \(0.222932\pi\) | |||||||
\(620\) | 2.15883 | 0.0867008 | ||||||||
\(621\) | −1.24698 | −0.0500396 | ||||||||
\(622\) | −21.3787 | −0.857206 | ||||||||
\(623\) | −10.2755 | −0.411677 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.8713 | 0.954089 | ||||||||
\(627\) | −3.59179 | −0.143442 | ||||||||
\(628\) | −12.2664 | −0.489481 | ||||||||
\(629\) | −8.35988 | −0.333330 | ||||||||
\(630\) | −1.19806 | −0.0477319 | ||||||||
\(631\) | −23.0901 | −0.919201 | −0.459600 | − | 0.888126i | \(-0.652007\pi\) | ||||
−0.459600 | + | 0.888126i | \(0.652007\pi\) | |||||||
\(632\) | −2.73556 | −0.108815 | ||||||||
\(633\) | 11.6775 | 0.464141 | ||||||||
\(634\) | −12.6407 | −0.502027 | ||||||||
\(635\) | −9.32736 | −0.370145 | ||||||||
\(636\) | 6.91185 | 0.274073 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.6770 | −0.541476 | ||||||||
\(639\) | −11.0707 | −0.437950 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 23.3948 | 0.924039 | 0.462019 | − | 0.886870i | \(-0.347125\pi\) | ||||
0.462019 | + | 0.886870i | \(0.347125\pi\) | |||||||
\(642\) | −10.1032 | −0.398742 | ||||||||
\(643\) | 6.00836 | 0.236947 | 0.118473 | − | 0.992957i | \(-0.462200\pi\) | ||||
0.118473 | + | 0.992957i | \(0.462200\pi\) | |||||||
\(644\) | 1.49396 | 0.0588702 | ||||||||
\(645\) | −3.43296 | −0.135173 | ||||||||
\(646\) | 1.58748 | 0.0624586 | ||||||||
\(647\) | −4.38511 | −0.172396 | −0.0861982 | − | 0.996278i | \(-0.527472\pi\) | ||||
−0.0861982 | + | 0.996278i | \(0.527472\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −40.3534 | −1.58401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.58642 | −0.101370 | ||||||||
\(652\) | 2.48858 | 0.0974604 | ||||||||
\(653\) | −20.6160 | −0.806765 | −0.403382 | − | 0.915032i | \(-0.632166\pi\) | ||||
−0.403382 | + | 0.915032i | \(0.632166\pi\) | |||||||
\(654\) | −10.5211 | −0.411408 | ||||||||
\(655\) | 4.62133 | 0.180570 | ||||||||
\(656\) | −0.198062 | −0.00773303 | ||||||||
\(657\) | −4.13706 | −0.161402 | ||||||||
\(658\) | 1.08085 | 0.0421359 | ||||||||
\(659\) | 18.4910 | 0.720306 | 0.360153 | − | 0.932893i | \(-0.382724\pi\) | ||||
0.360153 | + | 0.932893i | \(0.382724\pi\) | |||||||
\(660\) | 3.93900 | 0.153325 | ||||||||
\(661\) | −17.6420 | −0.686196 | −0.343098 | − | 0.939300i | \(-0.611476\pi\) | ||||
−0.343098 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(662\) | 20.5109 | 0.797180 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.5864 | 0.604870 | ||||||||
\(665\) | −1.09246 | −0.0423637 | ||||||||
\(666\) | 4.80194 | 0.186071 | ||||||||
\(667\) | −4.32975 | −0.167649 | ||||||||
\(668\) | −7.27950 | −0.281652 | ||||||||
\(669\) | 11.4004 | 0.440766 | ||||||||
\(670\) | −9.16852 | −0.354211 | ||||||||
\(671\) | −39.1021 | −1.50952 | ||||||||
\(672\) | 1.19806 | 0.0462163 | ||||||||
\(673\) | 17.1473 | 0.660981 | 0.330491 | − | 0.943809i | \(-0.392786\pi\) | ||||
0.330491 | + | 0.943809i | \(0.392786\pi\) | |||||||
\(674\) | −6.82371 | −0.262839 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7982 | 1.22210 | 0.611052 | − | 0.791590i | \(-0.290746\pi\) | ||||
0.611052 | + | 0.791590i | \(0.290746\pi\) | |||||||
\(678\) | −11.2131 | −0.430638 | ||||||||
\(679\) | −20.3642 | −0.781506 | ||||||||
\(680\) | −1.74094 | −0.0667620 | ||||||||
\(681\) | 8.86725 | 0.339794 | ||||||||
\(682\) | 8.50365 | 0.325622 | ||||||||
\(683\) | −6.32783 | −0.242128 | −0.121064 | − | 0.992645i | \(-0.538631\pi\) | ||||
−0.121064 | + | 0.992645i | \(0.538631\pi\) | |||||||
\(684\) | −0.911854 | −0.0348656 | ||||||||
\(685\) | −0.0760644 | −0.00290627 | ||||||||
\(686\) | 15.0532 | 0.574735 | ||||||||
\(687\) | 12.6136 | 0.481237 | ||||||||
\(688\) | 3.43296 | 0.130880 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.24698 | 0.0474717 | ||||||||
\(691\) | 15.1825 | 0.577570 | 0.288785 | − | 0.957394i | \(-0.406749\pi\) | ||||
0.288785 | + | 0.957394i | \(0.406749\pi\) | |||||||
\(692\) | 15.8485 | 0.602468 | ||||||||
\(693\) | −4.71917 | −0.179266 | ||||||||
\(694\) | 29.4741 | 1.11882 | ||||||||
\(695\) | 18.7017 | 0.709396 | ||||||||
\(696\) | −3.47219 | −0.131613 | ||||||||
\(697\) | −0.344814 | −0.0130608 | ||||||||
\(698\) | −34.5394 | −1.30734 | ||||||||
\(699\) | 23.4155 | 0.885656 | ||||||||
\(700\) | 1.19806 | 0.0452825 | ||||||||
\(701\) | −23.6528 | −0.893354 | −0.446677 | − | 0.894695i | \(-0.647393\pi\) | ||||
−0.446677 | + | 0.894695i | \(0.647393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37867 | 0.165145 | ||||||||
\(704\) | −3.93900 | −0.148457 | ||||||||
\(705\) | 0.902165 | 0.0339775 | ||||||||
\(706\) | 31.2295 | 1.17534 | ||||||||
\(707\) | 7.99138 | 0.300547 | ||||||||
\(708\) | −10.2446 | −0.385015 | ||||||||
\(709\) | 40.9353 | 1.53736 | 0.768678 | − | 0.639636i | \(-0.220915\pi\) | ||||
0.768678 | + | 0.639636i | \(0.220915\pi\) | |||||||
\(710\) | 11.0707 | 0.415476 | ||||||||
\(711\) | 2.73556 | 0.102592 | ||||||||
\(712\) | 8.57673 | 0.321426 | ||||||||
\(713\) | 2.69202 | 0.100817 | ||||||||
\(714\) | 2.08575 | 0.0780573 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.4819 | 0.690700 | ||||||||
\(717\) | 8.87263 | 0.331354 | ||||||||
\(718\) | 18.2524 | 0.681172 | ||||||||
\(719\) | 4.55363 | 0.169822 | 0.0849109 | − | 0.996389i | \(-0.472939\pi\) | ||||
0.0849109 | + | 0.996389i | \(0.472939\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 12.0183 | 0.447585 | ||||||||
\(722\) | 18.1685 | 0.676162 | ||||||||
\(723\) | 9.72886 | 0.361820 | ||||||||
\(724\) | 10.7041 | 0.397815 | ||||||||
\(725\) | −3.47219 | −0.128954 | ||||||||
\(726\) | 4.51573 | 0.167594 | ||||||||
\(727\) | 18.1612 | 0.673563 | 0.336781 | − | 0.941583i | \(-0.390662\pi\) | ||||
0.336781 | + | 0.941583i | \(0.390662\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.13706 | 0.153120 | ||||||||
\(731\) | 5.97657 | 0.221052 | ||||||||
\(732\) | −9.92692 | −0.366910 | ||||||||
\(733\) | −9.89115 | −0.365338 | −0.182669 | − | 0.983174i | \(-0.558474\pi\) | ||||
−0.182669 | + | 0.983174i | \(0.558474\pi\) | |||||||
\(734\) | 19.3773 | 0.715231 | ||||||||
\(735\) | 5.56465 | 0.205255 | ||||||||
\(736\) | −1.24698 | −0.0459643 | ||||||||
\(737\) | −36.1148 | −1.33031 | ||||||||
\(738\) | 0.198062 | 0.00729077 | ||||||||
\(739\) | 23.9608 | 0.881411 | 0.440706 | − | 0.897652i | \(-0.354728\pi\) | ||||
0.440706 | + | 0.897652i | \(0.354728\pi\) | |||||||
\(740\) | −4.80194 | −0.176523 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.28083 | 0.303999 | ||||||||
\(743\) | −46.6708 | −1.71219 | −0.856094 | − | 0.516821i | \(-0.827115\pi\) | ||||
−0.856094 | + | 0.516821i | \(0.827115\pi\) | |||||||
\(744\) | 2.15883 | 0.0791467 | ||||||||
\(745\) | −13.6799 | −0.501194 | ||||||||
\(746\) | 13.6280 | 0.498958 | ||||||||
\(747\) | −15.5864 | −0.570277 | ||||||||
\(748\) | −6.85756 | −0.250737 | ||||||||
\(749\) | −12.1043 | −0.442281 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −30.9168 | −1.12817 | −0.564084 | − | 0.825717i | \(-0.690771\pi\) | ||||
−0.564084 | + | 0.825717i | \(0.690771\pi\) | |||||||
\(752\) | −0.902165 | −0.0328986 | ||||||||
\(753\) | −29.8823 | −1.08897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.15883 | 0.0421743 | ||||||||
\(756\) | −1.19806 | −0.0435731 | ||||||||
\(757\) | 24.4566 | 0.888892 | 0.444446 | − | 0.895806i | \(-0.353401\pi\) | ||||
0.444446 | + | 0.895806i | \(0.353401\pi\) | |||||||
\(758\) | −1.32006 | −0.0479467 | ||||||||
\(759\) | 4.91185 | 0.178289 | ||||||||
\(760\) | 0.911854 | 0.0330764 | ||||||||
\(761\) | 20.5536 | 0.745069 | 0.372534 | − | 0.928018i | \(-0.378489\pi\) | ||||
0.372534 | + | 0.928018i | \(0.378489\pi\) | |||||||
\(762\) | −9.32736 | −0.337894 | ||||||||
\(763\) | −12.6049 | −0.456329 | ||||||||
\(764\) | 15.3623 | 0.555788 | ||||||||
\(765\) | 1.74094 | 0.0629438 | ||||||||
\(766\) | 25.5308 | 0.922465 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 21.0084 | 0.757581 | 0.378790 | − | 0.925482i | \(-0.376340\pi\) | ||||
0.378790 | + | 0.925482i | \(0.376340\pi\) | |||||||
\(770\) | 4.71917 | 0.170067 | ||||||||
\(771\) | 8.52111 | 0.306880 | ||||||||
\(772\) | 18.3207 | 0.659375 | ||||||||
\(773\) | 36.2626 | 1.30428 | 0.652138 | − | 0.758100i | \(-0.273872\pi\) | ||||
0.652138 | + | 0.758100i | \(0.273872\pi\) | |||||||
\(774\) | −3.43296 | −0.123395 | ||||||||
\(775\) | 2.15883 | 0.0775476 | ||||||||
\(776\) | 16.9976 | 0.610179 | ||||||||
\(777\) | 5.75302 | 0.206388 | ||||||||
\(778\) | 6.05967 | 0.217250 | ||||||||
\(779\) | 0.180604 | 0.00647081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.6075 | 1.56040 | ||||||||
\(782\) | −2.17092 | −0.0776318 | ||||||||
\(783\) | 3.47219 | 0.124086 | ||||||||
\(784\) | −5.56465 | −0.198737 | ||||||||
\(785\) | −12.2664 | −0.437805 | ||||||||
\(786\) | 4.62133 | 0.164838 | ||||||||
\(787\) | 1.55927 | 0.0555820 | 0.0277910 | − | 0.999614i | \(-0.491153\pi\) | ||||
0.0277910 | + | 0.999614i | \(0.491153\pi\) | |||||||
\(788\) | 2.31336 | 0.0824099 | ||||||||
\(789\) | 22.6450 | 0.806184 | ||||||||
\(790\) | −2.73556 | −0.0973269 | ||||||||
\(791\) | −13.4340 | −0.477659 | ||||||||
\(792\) | 3.93900 | 0.139966 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.99330 | 0.212694 | ||||||||
\(795\) | 6.91185 | 0.245138 | ||||||||
\(796\) | 6.36765 | 0.225695 | ||||||||
\(797\) | 5.16793 | 0.183058 | 0.0915288 | − | 0.995802i | \(-0.470825\pi\) | ||||
0.0915288 | + | 0.995802i | \(0.470825\pi\) | |||||||
\(798\) | −1.09246 | −0.0386726 | ||||||||
\(799\) | −1.57061 | −0.0555644 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −8.57673 | −0.303044 | ||||||||
\(802\) | 17.3773 | 0.613615 | ||||||||
\(803\) | 16.2959 | 0.575070 | ||||||||
\(804\) | −9.16852 | −0.323349 | ||||||||
\(805\) | 1.49396 | 0.0526551 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.02608 | 0.317733 | ||||||||
\(808\) | −6.67025 | −0.234659 | ||||||||
\(809\) | −31.8605 | −1.12016 | −0.560079 | − | 0.828440i | \(-0.689229\pi\) | ||||
−0.560079 | + | 0.828440i | \(0.689229\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 15.3056 | 0.537452 | 0.268726 | − | 0.963217i | \(-0.413397\pi\) | ||||
0.268726 | + | 0.963217i | \(0.413397\pi\) | |||||||
\(812\) | −4.15990 | −0.145984 | ||||||||
\(813\) | −8.59611 | −0.301479 | ||||||||
\(814\) | −18.9148 | −0.662965 | ||||||||
\(815\) | 2.48858 | 0.0871712 | ||||||||
\(816\) | −1.74094 | −0.0609450 | ||||||||
\(817\) | −3.13036 | −0.109517 | ||||||||
\(818\) | 29.3672 | 1.02680 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.198062 | −0.00691663 | ||||||||
\(821\) | −32.0248 | −1.11767 | −0.558836 | − | 0.829278i | \(-0.688752\pi\) | ||||
−0.558836 | + | 0.829278i | \(0.688752\pi\) | |||||||
\(822\) | −0.0760644 | −0.00265305 | ||||||||
\(823\) | −36.8571 | −1.28476 | −0.642379 | − | 0.766387i | \(-0.722052\pi\) | ||||
−0.642379 | + | 0.766387i | \(0.722052\pi\) | |||||||
\(824\) | −10.0315 | −0.349462 | ||||||||
\(825\) | 3.93900 | 0.137138 | ||||||||
\(826\) | −12.2737 | −0.427055 | ||||||||
\(827\) | 37.9269 | 1.31885 | 0.659424 | − | 0.751771i | \(-0.270800\pi\) | ||||
0.659424 | + | 0.751771i | \(0.270800\pi\) | |||||||
\(828\) | 1.24698 | 0.0433355 | ||||||||
\(829\) | −34.2349 | −1.18903 | −0.594514 | − | 0.804086i | \(-0.702655\pi\) | ||||
−0.594514 | + | 0.804086i | \(0.702655\pi\) | |||||||
\(830\) | 15.5864 | 0.541012 | ||||||||
\(831\) | −6.31527 | −0.219074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.68771 | −0.335659 | ||||||||
\(834\) | 18.7017 | 0.647587 | ||||||||
\(835\) | −7.27950 | −0.251918 | ||||||||
\(836\) | 3.59179 | 0.124225 | ||||||||
\(837\) | −2.15883 | −0.0746202 | ||||||||
\(838\) | 26.5472 | 0.917057 | ||||||||
\(839\) | −18.7318 | −0.646695 | −0.323347 | − | 0.946280i | \(-0.604808\pi\) | ||||
−0.323347 | + | 0.946280i | \(0.604808\pi\) | |||||||
\(840\) | 1.19806 | 0.0413371 | ||||||||
\(841\) | −16.9439 | −0.584273 | ||||||||
\(842\) | −31.0834 | −1.07120 | ||||||||
\(843\) | 21.7409 | 0.748798 | ||||||||
\(844\) | −11.6775 | −0.401958 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.902165 | 0.0310171 | ||||||||
\(847\) | 5.41013 | 0.185894 | ||||||||
\(848\) | −6.91185 | −0.237354 | ||||||||
\(849\) | −12.9487 | −0.444398 | ||||||||
\(850\) | −1.74094 | −0.0597137 | ||||||||
\(851\) | −5.98792 | −0.205263 | ||||||||
\(852\) | 11.0707 | 0.379276 | ||||||||
\(853\) | 4.64071 | 0.158895 | 0.0794475 | − | 0.996839i | \(-0.474684\pi\) | ||||
0.0794475 | + | 0.996839i | \(0.474684\pi\) | |||||||
\(854\) | −11.8931 | −0.406972 | ||||||||
\(855\) | −0.911854 | −0.0311847 | ||||||||
\(856\) | 10.1032 | 0.345321 | ||||||||
\(857\) | 11.1347 | 0.380353 | 0.190177 | − | 0.981750i | \(-0.439094\pi\) | ||||
0.190177 | + | 0.981750i | \(0.439094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9661 | 0.988312 | 0.494156 | − | 0.869373i | \(-0.335477\pi\) | ||||
0.494156 | + | 0.869373i | \(0.335477\pi\) | |||||||
\(860\) | 3.43296 | 0.117063 | ||||||||
\(861\) | 0.237291 | 0.00808685 | ||||||||
\(862\) | 36.1226 | 1.23034 | ||||||||
\(863\) | −33.1371 | −1.12800 | −0.563999 | − | 0.825775i | \(-0.690738\pi\) | ||||
−0.563999 | + | 0.825775i | \(0.690738\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 15.8485 | 0.538864 | ||||||||
\(866\) | 35.2868 | 1.19909 | ||||||||
\(867\) | 13.9691 | 0.474417 | ||||||||
\(868\) | 2.58642 | 0.0877887 | ||||||||
\(869\) | −10.7754 | −0.365530 | ||||||||
\(870\) | −3.47219 | −0.117718 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.5211 | 0.356290 | ||||||||
\(873\) | −16.9976 | −0.575282 | ||||||||
\(874\) | 1.13706 | 0.0384617 | ||||||||
\(875\) | 1.19806 | 0.0405019 | ||||||||
\(876\) | 4.13706 | 0.139778 | ||||||||
\(877\) | −19.1371 | −0.646213 | −0.323106 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323106 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(878\) | 32.0170 | 1.08052 | ||||||||
\(879\) | 27.3056 | 0.920995 | ||||||||
\(880\) | −3.93900 | −0.132784 | ||||||||
\(881\) | −40.3387 | −1.35905 | −0.679523 | − | 0.733655i | \(-0.737813\pi\) | ||||
−0.679523 | + | 0.733655i | \(0.737813\pi\) | |||||||
\(882\) | 5.56465 | 0.187371 | ||||||||
\(883\) | −4.31336 | −0.145156 | −0.0725780 | − | 0.997363i | \(-0.523123\pi\) | ||||
−0.0725780 | + | 0.997363i | \(0.523123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.2446 | −0.344368 | ||||||||
\(886\) | 23.5948 | 0.792682 | ||||||||
\(887\) | −9.38404 | −0.315085 | −0.157543 | − | 0.987512i | \(-0.550357\pi\) | ||||
−0.157543 | + | 0.987512i | \(0.550357\pi\) | |||||||
\(888\) | −4.80194 | −0.161142 | ||||||||
\(889\) | −11.1748 | −0.374789 | ||||||||
\(890\) | 8.57673 | 0.287493 | ||||||||
\(891\) | −3.93900 | −0.131962 | ||||||||
\(892\) | −11.4004 | −0.381715 | ||||||||
\(893\) | 0.822643 | 0.0275287 | ||||||||
\(894\) | −13.6799 | −0.457526 | ||||||||
\(895\) | 18.4819 | 0.617781 | ||||||||
\(896\) | −1.19806 | −0.0400245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.8374 | −0.661984 | ||||||||
\(899\) | −7.49588 | −0.250002 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −12.0331 | −0.400881 | ||||||||
\(902\) | −0.780167 | −0.0259767 | ||||||||
\(903\) | −4.11290 | −0.136869 | ||||||||
\(904\) | 11.2131 | 0.372943 | ||||||||
\(905\) | 10.7041 | 0.355816 | ||||||||
\(906\) | 1.15883 | 0.0384997 | ||||||||
\(907\) | 14.2131 | 0.471939 | 0.235970 | − | 0.971760i | \(-0.424173\pi\) | ||||
0.235970 | + | 0.971760i | \(0.424173\pi\) | |||||||
\(908\) | −8.86725 | −0.294270 | ||||||||
\(909\) | 6.67025 | 0.221238 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2707 | 1.33423 | 0.667113 | − | 0.744956i | \(-0.267530\pi\) | ||||
0.667113 | + | 0.744956i | \(0.267530\pi\) | |||||||
\(912\) | 0.911854 | 0.0301945 | ||||||||
\(913\) | 61.3949 | 2.03188 | ||||||||
\(914\) | −26.5284 | −0.877482 | ||||||||
\(915\) | −9.92692 | −0.328174 | ||||||||
\(916\) | −12.6136 | −0.416764 | ||||||||
\(917\) | 5.53665 | 0.182836 | ||||||||
\(918\) | 1.74094 | 0.0574595 | ||||||||
\(919\) | 7.03577 | 0.232089 | 0.116044 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116044 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(920\) | −1.24698 | −0.0411117 | ||||||||
\(921\) | −24.9124 | −0.820893 | ||||||||
\(922\) | −12.2717 | −0.404148 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.71917 | 0.155249 | ||||||||
\(925\) | −4.80194 | −0.157887 | ||||||||
\(926\) | −12.6455 | −0.415557 | ||||||||
\(927\) | 10.0315 | 0.329476 | ||||||||
\(928\) | 3.47219 | 0.113980 | ||||||||
\(929\) | 21.3575 | 0.700716 | 0.350358 | − | 0.936616i | \(-0.386060\pi\) | ||||
0.350358 | + | 0.936616i | \(0.386060\pi\) | |||||||
\(930\) | 2.15883 | 0.0707909 | ||||||||
\(931\) | 5.07415 | 0.166298 | ||||||||
\(932\) | −23.4155 | −0.767000 | ||||||||
\(933\) | −21.3787 | −0.699906 | ||||||||
\(934\) | −11.3870 | −0.372595 | ||||||||
\(935\) | −6.85756 | −0.224266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.7396 | 1.36357 | 0.681787 | − | 0.731551i | \(-0.261203\pi\) | ||||
0.681787 | + | 0.731551i | \(0.261203\pi\) | |||||||
\(938\) | −10.9845 | −0.358655 | ||||||||
\(939\) | 23.8713 | 0.779010 | ||||||||
\(940\) | −0.902165 | −0.0294254 | ||||||||
\(941\) | 26.2078 | 0.854348 | 0.427174 | − | 0.904169i | \(-0.359509\pi\) | ||||
0.427174 | + | 0.904169i | \(0.359509\pi\) | |||||||
\(942\) | −12.2664 | −0.399660 | ||||||||
\(943\) | −0.246980 | −0.00804276 | ||||||||
\(944\) | 10.2446 | 0.333433 | ||||||||
\(945\) | −1.19806 | −0.0389730 | ||||||||
\(946\) | 13.5224 | 0.439652 | ||||||||
\(947\) | 3.15239 | 0.102439 | 0.0512195 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512195 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(948\) | −2.73556 | −0.0888469 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.911854 | 0.0295845 | ||||||||
\(951\) | −12.6407 | −0.409903 | ||||||||
\(952\) | −2.08575 | −0.0675996 | ||||||||
\(953\) | −3.56060 | −0.115339 | −0.0576695 | − | 0.998336i | \(-0.518367\pi\) | ||||
−0.0576695 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(954\) | 6.91185 | 0.223780 | ||||||||
\(955\) | 15.3623 | 0.497111 | ||||||||
\(956\) | −8.87263 | −0.286961 | ||||||||
\(957\) | −13.6770 | −0.442113 | ||||||||
\(958\) | 18.8431 | 0.608792 | ||||||||
\(959\) | −0.0911299 | −0.00294274 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −26.3394 | −0.849659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.1032 | −0.325571 | ||||||||
\(964\) | −9.72886 | −0.313345 | ||||||||
\(965\) | 18.3207 | 0.589763 | ||||||||
\(966\) | 1.49396 | 0.0480673 | ||||||||
\(967\) | 7.26875 | 0.233747 | 0.116874 | − | 0.993147i | \(-0.462713\pi\) | ||||
0.116874 | + | 0.993147i | \(0.462713\pi\) | |||||||
\(968\) | −4.51573 | −0.145141 | ||||||||
\(969\) | 1.58748 | 0.0509973 | ||||||||
\(970\) | 16.9976 | 0.545760 | ||||||||
\(971\) | −9.53511 | −0.305996 | −0.152998 | − | 0.988226i | \(-0.548893\pi\) | ||||
−0.152998 | + | 0.988226i | \(0.548893\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 22.4058 | 0.718297 | ||||||||
\(974\) | 27.6383 | 0.885589 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.92692 | 0.317753 | ||||||||
\(977\) | 17.5700 | 0.562115 | 0.281057 | − | 0.959691i | \(-0.409315\pi\) | ||||
0.281057 | + | 0.959691i | \(0.409315\pi\) | |||||||
\(978\) | 2.48858 | 0.0795761 | ||||||||
\(979\) | 33.7837 | 1.07973 | ||||||||
\(980\) | −5.56465 | −0.177756 | ||||||||
\(981\) | −10.5211 | −0.335913 | ||||||||
\(982\) | 13.9866 | 0.446330 | ||||||||
\(983\) | 43.4935 | 1.38723 | 0.693613 | − | 0.720347i | \(-0.256018\pi\) | ||||
0.693613 | + | 0.720347i | \(0.256018\pi\) | |||||||
\(984\) | −0.198062 | −0.00631399 | ||||||||
\(985\) | 2.31336 | 0.0737096 | ||||||||
\(986\) | 6.04487 | 0.192508 | ||||||||
\(987\) | 1.08085 | 0.0344038 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.28083 | 0.136123 | ||||||||
\(990\) | 3.93900 | 0.125190 | ||||||||
\(991\) | 38.8232 | 1.23326 | 0.616630 | − | 0.787253i | \(-0.288497\pi\) | ||||
0.616630 | + | 0.787253i | \(0.288497\pi\) | |||||||
\(992\) | −2.15883 | −0.0685430 | ||||||||
\(993\) | 20.5109 | 0.650895 | ||||||||
\(994\) | 13.2634 | 0.420689 | ||||||||
\(995\) | 6.36765 | 0.201868 | ||||||||
\(996\) | 15.5864 | 0.493875 | ||||||||
\(997\) | −21.9807 | −0.696137 | −0.348069 | − | 0.937469i | \(-0.613162\pi\) | ||||
−0.348069 | + | 0.937469i | \(0.613162\pi\) | |||||||
\(998\) | −8.87071 | −0.280797 | ||||||||
\(999\) | 4.80194 | 0.151927 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5070.2.a.bl.1.1 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.v.1351.4 | 6 | |||
13.8 | odd | 4 | 5070.2.b.v.1351.3 | 6 | |||
13.12 | even | 2 | 5070.2.a.bs.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bl.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.bs.1.3 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.v.1351.3 | 6 | 13.8 | odd | 4 | |||
5070.2.b.v.1351.4 | 6 | 13.5 | odd | 4 |