Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(19,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 4, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.p (of order \(8\), degree \(4\), minimal) |
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: | no |
Analytic conductor: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{8}]$ |
Embedding invariants
Embedding label | 83.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.83 |
Dual form | 136.3.p.a.59.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | ||||
\(3\) | 1.53553 | + | 3.70711i | 0.511845 | + | 1.23570i | 0.942809 | + | 0.333333i | \(0.108173\pi\) |
−0.430964 | + | 0.902369i | \(0.641827\pi\) | |||||||
\(4\) | 4.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(6\) | 3.07107 | − | 7.41421i | 0.511845 | − | 1.23570i | ||||
\(7\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(8\) | 5.65685 | − | 5.65685i | 0.707107 | − | 0.707107i | ||||
\(9\) | −5.02082 | + | 5.02082i | −0.557868 | + | 0.557868i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.05025 | + | 19.4350i | −0.731841 | + | 1.76682i | −0.0954775 | + | 0.995432i | \(0.530438\pi\) |
−0.636364 | + | 0.771389i | \(0.719562\pi\) | |||||||
\(12\) | −14.8284 | + | 6.14214i | −1.23570 | + | 0.511845i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −1.00000 | ||||||||
\(17\) | −12.7071 | + | 11.2929i | −0.747477 | + | 0.664288i | ||||
\(18\) | 14.2010 | 0.788945 | ||||||||
\(19\) | 12.0000 | + | 12.0000i | 0.631579 | + | 0.631579i | 0.948464 | − | 0.316885i | \(-0.102637\pi\) |
−0.316885 | + | 0.948464i | \(0.602637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 38.8701 | − | 16.1005i | 1.76682 | − | 0.731841i | ||||
\(23\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(24\) | 29.6569 | + | 12.2843i | 1.23570 | + | 0.511845i | ||||
\(25\) | 17.6777 | − | 17.6777i | 0.707107 | − | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.04163 | + | 2.91674i | 0.260801 | + | 0.108027i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(32\) | 22.6274 | + | 22.6274i | 0.707107 | + | 0.707107i | ||||
\(33\) | −84.4092 | −2.55785 | ||||||||
\(34\) | 33.9411 | + | 2.00000i | 0.998268 | + | 0.0588235i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −20.0833 | − | 20.0833i | −0.557868 | − | 0.557868i | ||||
\(37\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(38\) | − | 33.9411i | − | 0.893188i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −41.6777 | − | 17.2635i | −1.01653 | − | 0.421060i | −0.188696 | − | 0.982036i | \(-0.560426\pi\) |
−0.827832 | + | 0.560976i | \(0.810426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.4264 | − | 49.4264i | 1.14945 | − | 1.14945i | 0.162791 | − | 0.986661i | \(-0.447950\pi\) |
0.986661 | − | 0.162791i | \(-0.0520495\pi\) | |||||||
\(44\) | −77.7401 | − | 32.2010i | −1.76682 | − | 0.731841i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −24.5685 | − | 59.3137i | −0.511845 | − | 1.23570i | ||||
\(49\) | 34.6482 | + | 34.6482i | 0.707107 | + | 0.707107i | ||||
\(50\) | −50.0000 | −1.00000 | ||||||||
\(51\) | −61.3762 | − | 29.7660i | −1.20345 | − | 0.583647i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | −5.83348 | − | 14.0833i | −0.108027 | − | 0.260801i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26.0589 | + | 62.9117i | −0.457173 | + | 1.10371i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 83.4264 | − | 83.4264i | 1.41401 | − | 1.41401i | 0.694915 | − | 0.719092i | \(-0.255442\pi\) |
0.719092 | − | 0.694915i | \(-0.244558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 64.0000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 119.373 | + | 119.373i | 1.80868 | + | 1.80868i | ||||
\(67\) | 40.1594 | 0.599394 | 0.299697 | − | 0.954034i | \(-0.403114\pi\) | ||||
0.299697 | + | 0.954034i | \(0.403114\pi\) | |||||||
\(68\) | −45.1716 | − | 50.8284i | −0.664288 | − | 0.747477i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(72\) | 56.8040i | 0.788945i | ||||||||
\(73\) | −21.2340 | + | 8.79542i | −0.290877 | + | 0.120485i | −0.523350 | − | 0.852118i | \(-0.675318\pi\) |
0.232473 | + | 0.972603i | \(0.425318\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 92.6777 | + | 38.3883i | 1.23570 | + | 0.511845i | ||||
\(76\) | −48.0000 | + | 48.0000i | −0.631579 | + | 0.631579i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 94.4874i | 1.16651i | ||||||||
\(82\) | 34.5269 | + | 83.3553i | 0.421060 | + | 1.01653i | ||||
\(83\) | 104.456 | + | 104.456i | 1.25850 | + | 1.25850i | 0.951807 | + | 0.306697i | \(0.0992238\pi\) |
0.306697 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −139.799 | −1.62557 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 64.4020 | + | 155.480i | 0.731841 | + | 1.76682i | ||||
\(89\) | − | 175.238i | − | 1.96896i | −0.175492 | − | 0.984481i | \(-0.556152\pi\) | ||
0.175492 | − | 0.984481i | \(-0.443848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −49.1371 | + | 118.627i | −0.511845 | + | 1.23570i | ||||
\(97\) | 140.234 | − | 58.0868i | 1.44571 | − | 0.598833i | 0.484536 | − | 0.874771i | \(-0.338988\pi\) |
0.961175 | + | 0.275938i | \(0.0889884\pi\) | |||||||
\(98\) | − | 98.0000i | − | 1.00000i | ||||||
\(99\) | −57.1609 | − | 137.999i | −0.577382 | − | 1.39392i | ||||
\(100\) | 70.7107 | + | 70.7107i | 0.707107 | + | 0.707107i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 44.7035 | + | 128.894i | 0.438270 | + | 1.26367i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −193.933 | + | 80.3295i | −1.81245 | + | 0.750743i | −0.831776 | + | 0.555112i | \(0.812675\pi\) |
−0.980678 | + | 0.195631i | \(0.937325\pi\) | |||||||
\(108\) | −11.6670 | + | 28.1665i | −0.108027 | + | 0.260801i | ||||
\(109\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.82486 | + | 11.6482i | −0.0426978 | + | 0.103082i | −0.943790 | − | 0.330547i | \(-0.892767\pi\) |
0.901092 | + | 0.433628i | \(0.142767\pi\) | |||||||
\(114\) | 125.823 | − | 52.1177i | 1.10371 | − | 0.457173i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −235.966 | −1.99971 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −227.354 | − | 227.354i | −1.87896 | − | 1.87896i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 181.012i | − | 1.47164i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −90.5097 | + | 90.5097i | −0.707107 | + | 0.707107i | ||||
\(129\) | 259.125 | + | 107.333i | 2.00872 | + | 0.832039i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −195.359 | + | 80.9203i | −1.49129 | + | 0.617712i | −0.971597 | − | 0.236641i | \(-0.923953\pi\) |
−0.519692 | + | 0.854354i | \(0.673953\pi\) | |||||||
\(132\) | − | 337.637i | − | 2.55785i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −56.7939 | − | 56.7939i | −0.423835 | − | 0.423835i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.00000 | + | 135.765i | −0.0588235 | + | 0.998268i | ||||
\(137\) | 135.765 | 0.990982 | 0.495491 | − | 0.868613i | \(-0.334988\pi\) | ||||
0.495491 | + | 0.868613i | \(0.334988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 45.4939 | + | 109.832i | 0.327294 | + | 0.790158i | 0.998791 | + | 0.0491511i | \(0.0156516\pi\) |
−0.671497 | + | 0.741007i | \(0.734348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 80.3330 | − | 80.3330i | 0.557868 | − | 0.557868i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 42.4680 | + | 17.5908i | 0.290877 | + | 0.120485i | ||||
\(147\) | −75.2412 | + | 181.648i | −0.511845 | + | 1.23570i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −76.7767 | − | 185.355i | −0.511845 | − | 1.23570i | ||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 135.765 | 0.893188 | ||||||||
\(153\) | 7.10051 | − | 120.500i | 0.0464085 | − | 0.787579i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 133.625 | − | 133.625i | 0.824848 | − | 0.824848i | ||||
\(163\) | 256.844 | + | 106.388i | 1.57573 | + | 0.652689i | 0.987730 | − | 0.156171i | \(-0.0499150\pi\) |
0.588001 | + | 0.808860i | \(0.299915\pi\) | |||||||
\(164\) | 69.0538 | − | 166.711i | 0.421060 | − | 1.01653i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 295.446i | − | 1.77979i | ||||||
\(167\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −120.500 | −0.704676 | ||||||||
\(172\) | 197.706 | + | 197.706i | 1.14945 | + | 1.14945i | ||||
\(173\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 128.804 | − | 310.960i | 0.731841 | − | 1.76682i | ||||
\(177\) | 437.375 | + | 181.167i | 2.47104 | + | 1.02354i | ||||
\(178\) | −247.823 | + | 247.823i | −1.39227 | + | 1.39227i | ||||
\(179\) | −252.000 | + | 252.000i | −1.40782 | + | 1.40782i | −0.636755 | + | 0.771066i | \(0.719724\pi\) |
−0.771066 | + | 0.636755i | \(0.780276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −117.182 | − | 337.874i | −0.626643 | − | 1.80681i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 237.255 | − | 98.2742i | 1.23570 | − | 0.511845i | ||||
\(193\) | −89.3244 | + | 215.648i | −0.462821 | + | 1.11735i | 0.504413 | + | 0.863462i | \(0.331709\pi\) |
−0.967234 | + | 0.253886i | \(0.918291\pi\) | |||||||
\(194\) | −280.468 | − | 116.174i | −1.44571 | − | 0.598833i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −138.593 | + | 138.593i | −0.707107 | + | 0.707107i | ||||
\(197\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(198\) | −114.322 | + | 275.997i | −0.577382 | + | 1.39392i | ||||
\(199\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(200\) | − | 200.000i | − | 1.00000i | ||||||
\(201\) | 61.6661 | + | 148.875i | 0.306796 | + | 0.740672i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 119.064 | − | 245.505i | 0.583647 | − | 1.20345i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −329.823 | + | 136.617i | −1.57810 | + | 0.653671i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −384.094 | − | 159.097i | −1.82035 | − | 0.754014i | −0.975844 | − | 0.218469i | \(-0.929894\pi\) |
−0.844507 | − | 0.535545i | \(-0.820106\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 387.865 | + | 160.659i | 1.81245 | + | 0.750743i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 56.3330 | − | 23.3339i | 0.260801 | − | 0.108027i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −65.2111 | − | 65.2111i | −0.297768 | − | 0.297768i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 177.513i | 0.788945i | ||||||||
\(226\) | 23.2965 | − | 9.64971i | 0.103082 | − | 0.0426978i | ||||
\(227\) | 145.258 | − | 350.685i | 0.639905 | − | 1.54487i | −0.186900 | − | 0.982379i | \(-0.559844\pi\) |
0.826805 | − | 0.562488i | \(-0.190156\pi\) | |||||||
\(228\) | −251.647 | − | 104.235i | −1.10371 | − | 0.457173i | ||||
\(229\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 430.442 | − | 178.295i | 1.84739 | − | 0.765215i | 0.916061 | − | 0.401039i | \(-0.131351\pi\) |
0.931330 | − | 0.364175i | \(-0.118649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 333.706 | + | 333.706i | 1.41401 | + | 1.41401i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −184.411 | − | 445.207i | −0.765189 | − | 1.84733i | −0.402490 | − | 0.915425i | \(-0.631855\pi\) |
−0.362700 | − | 0.931906i | \(-0.618145\pi\) | |||||||
\(242\) | 643.054i | 2.65725i | ||||||||
\(243\) | −286.900 | + | 118.838i | −1.18066 | + | 0.489045i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −255.990 | + | 255.990i | −1.04061 | + | 1.04061i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −226.833 | + | 547.624i | −0.910978 | + | 2.19930i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 461.512i | 1.83869i | 0.393450 | + | 0.919346i | \(0.371282\pi\) | ||||
−0.393450 | + | 0.919346i | \(0.628718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | −23.2944 | − | 23.2944i | −0.0906396 | − | 0.0906396i | 0.660333 | − | 0.750973i | \(-0.270415\pi\) |
−0.750973 | + | 0.660333i | \(0.770415\pi\) | |||||||
\(258\) | −214.666 | − | 518.250i | −0.832039 | − | 2.00872i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 390.718 | + | 161.841i | 1.49129 | + | 0.617712i | ||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | −477.490 | + | 477.490i | −1.80868 | + | 1.80868i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 649.624 | − | 269.083i | 2.43305 | − | 1.00780i | ||||
\(268\) | 160.638i | 0.599394i | ||||||||
\(269\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 203.314 | − | 180.686i | 0.747477 | − | 0.664288i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −192.000 | − | 192.000i | −0.700730 | − | 0.700730i | ||||
\(275\) | 201.256 | + | 485.876i | 0.731841 | + | 1.76682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(278\) | 90.9878 | − | 219.664i | 0.327294 | − | 0.790158i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 360.000 | − | 360.000i | 1.28114 | − | 1.28114i | 0.341118 | − | 0.940020i | \(-0.389194\pi\) |
0.940020 | − | 0.341118i | \(-0.110806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 185.991 | − | 449.023i | 0.657213 | − | 1.58665i | −0.144876 | − | 0.989450i | \(-0.546278\pi\) |
0.802090 | − | 0.597204i | \(-0.203722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −227.216 | −0.788945 | ||||||||
\(289\) | 33.9411 | − | 287.000i | 0.117443 | − | 0.993080i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 430.668 | + | 430.668i | 1.47996 | + | 1.47996i | ||||
\(292\) | −35.1817 | − | 84.9361i | −0.120485 | − | 0.290877i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 363.296 | − | 150.482i | 1.23570 | − | 0.511845i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −113.374 | + | 113.374i | −0.381730 | + | 0.381730i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −153.553 | + | 370.711i | −0.511845 | + | 1.23570i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −192.000 | − | 192.000i | −0.631579 | − | 0.631579i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −180.454 | + | 160.370i | −0.589718 | + | 0.524087i | ||||
\(307\) | −542.000 | −1.76547 | −0.882736 | − | 0.469869i | \(-0.844301\pi\) | ||||
−0.882736 | + | 0.469869i | \(0.844301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 328.969 | + | 136.263i | 1.05102 | + | 0.435347i | 0.840256 | − | 0.542191i | \(-0.182405\pi\) |
0.210764 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −595.580 | − | 595.580i | −1.85539 | − | 1.85539i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −288.000 | − | 16.9706i | −0.891641 | − | 0.0525404i | ||||
\(324\) | −377.949 | −1.16651 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −212.777 | − | 513.688i | −0.652689 | − | 1.57573i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −333.421 | + | 138.108i | −1.01653 | + | 0.421060i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 337.926 | − | 337.926i | 1.02092 | − | 1.02092i | 0.0211480 | − | 0.999776i | \(-0.493268\pi\) |
0.999776 | − | 0.0211480i | \(-0.00673213\pi\) | |||||||
\(332\) | −417.823 | + | 417.823i | −1.25850 | + | 1.25850i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 99.4106 | + | 239.999i | 0.294987 | + | 0.712162i | 0.999996 | + | 0.00296297i | \(0.000943144\pi\) |
−0.705009 | + | 0.709199i | \(0.749057\pi\) | |||||||
\(338\) | 239.002 | + | 239.002i | 0.707107 | + | 0.707107i | ||||
\(339\) | −50.5900 | −0.149233 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 170.412 | + | 170.412i | 0.498281 | + | 0.498281i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 559.196i | − | 1.62557i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 420.947 | + | 174.362i | 1.21310 | + | 0.502484i | 0.895211 | − | 0.445643i | \(-0.147025\pi\) |
0.317892 | + | 0.948127i | \(0.397025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −621.921 | + | 257.608i | −1.76682 | + | 0.731841i | ||||
\(353\) | − | 342.821i | − | 0.971165i | −0.874191 | − | 0.485583i | \(-0.838608\pi\) | ||
0.874191 | − | 0.485583i | \(-0.161392\pi\) | |||||||
\(354\) | −362.333 | − | 874.749i | −1.02354 | − | 2.47104i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 700.950 | 1.96896 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 712.764 | 1.99096 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 73.0000i | − | 0.202216i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 493.715 | − | 1191.93i | 1.36010 | − | 3.28357i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 295.933 | − | 122.579i | 0.801985 | − | 0.332193i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | −312.105 | + | 643.546i | −0.834505 | + | 1.72071i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.6827 | − | 13.5376i | 0.0862341 | − | 0.0357193i | −0.339149 | − | 0.940733i | \(-0.610139\pi\) |
0.425383 | + | 0.905013i | \(0.360139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | −474.510 | − | 196.548i | −1.23570 | − | 0.511845i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 431.296 | − | 178.649i | 1.11735 | − | 0.462821i | ||||
\(387\) | 496.322i | 1.28249i | ||||||||
\(388\) | 232.347 | + | 560.936i | 0.598833 | + | 1.44571i | ||||
\(389\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 392.000 | 1.00000 | ||||||||
\(393\) | −599.960 | − | 599.960i | −1.52662 | − | 1.52662i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 551.994 | − | 228.643i | 1.39392 | − | 0.577382i | ||||
\(397\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −282.843 | + | 282.843i | −0.707107 | + | 0.707107i | ||||
\(401\) | −569.822 | − | 236.028i | −1.42100 | − | 0.588598i | −0.465890 | − | 0.884843i | \(-0.654266\pi\) |
−0.955112 | + | 0.296244i | \(0.904266\pi\) | |||||||
\(402\) | 123.332 | − | 297.750i | 0.306796 | − | 0.740672i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −515.578 | + | 178.814i | −1.26367 | + | 0.438270i | ||||
\(409\) | −764.174 | −1.86840 | −0.934198 | − | 0.356756i | \(-0.883883\pi\) | ||||
−0.934198 | + | 0.356756i | \(0.883883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 208.471 | + | 503.294i | 0.507229 | + | 1.22456i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −337.302 | + | 337.302i | −0.808877 | + | 0.808877i | ||||
\(418\) | 659.647 | + | 273.235i | 1.57810 | + | 0.653671i | ||||
\(419\) | 84.8005 | − | 204.726i | 0.202388 | − | 0.488607i | −0.789799 | − | 0.613365i | \(-0.789815\pi\) |
0.992187 | + | 0.124758i | \(0.0398154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 318.194 | + | 768.188i | 0.754014 | + | 1.82035i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.0000 | + | 424.264i | −0.0588235 | + | 0.998268i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −321.318 | − | 775.730i | −0.750743 | − | 1.81245i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(432\) | −112.666 | − | 46.6678i | −0.260801 | − | 0.108027i | ||||
\(433\) | −456.000 | + | 456.000i | −1.05312 | + | 1.05312i | −0.0546100 | + | 0.998508i | \(0.517392\pi\) |
−0.998508 | + | 0.0546100i | \(0.982608\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 184.445i | 0.421107i | ||||||||
\(439\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −347.925 | −0.788945 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −536.840 | −1.21183 | −0.605914 | − | 0.795530i | \(-0.707192\pi\) | ||||
−0.605914 | + | 0.795530i | \(0.707192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 823.177 | + | 340.971i | 1.83336 | + | 0.759401i | 0.964365 | + | 0.264574i | \(0.0852315\pi\) |
0.868992 | + | 0.494827i | \(0.164769\pi\) | |||||||
\(450\) | 251.041 | − | 251.041i | 0.557868 | − | 0.557868i | ||||
\(451\) | 671.032 | − | 671.032i | 1.48787 | − | 1.48787i | ||||
\(452\) | −46.5929 | − | 19.2994i | −0.103082 | − | 0.0426978i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −701.370 | + | 290.517i | −1.54487 | + | 0.639905i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 208.471 | + | 503.294i | 0.457173 | + | 1.10371i | ||||
\(457\) | 624.000 | + | 624.000i | 1.36543 | + | 1.36543i | 0.866840 | + | 0.498587i | \(0.166148\pi\) |
0.498587 | + | 0.866840i | \(0.333852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −122.417 | + | 42.4571i | −0.266704 | + | 0.0924991i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −860.884 | − | 356.590i | −1.84739 | − | 0.765215i | ||||
\(467\) | −660.000 | + | 660.000i | −1.41328 | + | 1.41328i | −0.680898 | + | 0.732379i | \(0.738410\pi\) |
−0.732379 | + | 0.680898i | \(0.761590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 943.862i | − | 1.99971i | ||||||
\(473\) | 562.709 | + | 1358.50i | 1.18966 | + | 2.87209i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 424.264 | 0.893188 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −368.821 | + | 890.413i | −0.765189 | + | 1.84733i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 909.415 | − | 909.415i | 1.87896 | − | 1.87896i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 573.800 | + | 237.676i | 1.18066 | + | 0.489045i | ||||
\(487\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1115.51i | 2.28121i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 420.000 | + | 420.000i | 0.855397 | + | 0.855397i | 0.990792 | − | 0.135395i | \(-0.0432302\pi\) |
−0.135395 | + | 0.990792i | \(0.543230\pi\) | |||||||
\(492\) | 724.049 | 1.47164 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1095.25 | − | 453.667i | 2.19930 | − | 0.910978i | ||||
\(499\) | −92.5498 | + | 223.435i | −0.185471 | + | 0.447766i | −0.989078 | − | 0.147394i | \(-0.952911\pi\) |
0.803607 | + | 0.595160i | \(0.202911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 652.676 | − | 652.676i | 1.30015 | − | 1.30015i | ||||
\(503\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −259.505 | − | 626.501i | −0.511845 | − | 1.23570i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −362.039 | − | 362.039i | −0.707107 | − | 0.707107i | ||||
\(513\) | 49.4987 | + | 119.500i | 0.0964887 | + | 0.232944i | ||||
\(514\) | 65.8864i | 0.128184i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −429.332 | + | 1036.50i | −0.832039 | + | 2.00872i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 243.325 | − | 587.439i | 0.467035 | − | 1.12752i | −0.498416 | − | 0.866938i | \(-0.666085\pi\) |
0.965451 | − | 0.260584i | \(-0.0839152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 402.572i | − | 0.769735i | −0.922972 | − | 0.384868i | \(-0.874247\pi\) | ||
0.922972 | − | 0.384868i | \(-0.125753\pi\) | |||||||
\(524\) | −323.681 | − | 781.436i | −0.617712 | − | 1.49129i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1350.55 | 2.55785 | ||||||||
\(529\) | −374.059 | − | 374.059i | −0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 837.737i | 1.57766i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1299.25 | − | 538.167i | −2.43305 | − | 1.00780i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 227.176 | − | 227.176i | 0.423835 | − | 0.423835i | ||||
\(537\) | −1321.15 | − | 547.236i | −2.46023 | − | 1.01906i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −952.316 | + | 394.462i | −1.76682 | + | 0.731841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −543.058 | − | 32.0000i | −0.998268 | − | 0.0588235i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 418.493 | + | 1010.33i | 0.765070 | + | 1.84704i | 0.408284 | + | 0.912855i | \(0.366127\pi\) |
0.356785 | + | 0.934186i | \(0.383873\pi\) | |||||||
\(548\) | 543.058i | 0.990982i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 402.513 | − | 971.751i | 0.731841 | − | 1.76682i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −439.328 | + | 181.976i | −0.790158 | + | 0.327294i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1072.60 | − | 953.224i | 1.91194 | − | 1.69915i | ||||
\(562\) | −1018.23 | −1.81180 | ||||||||
\(563\) | −438.543 | − | 438.543i | −0.778940 | − | 0.778940i | 0.200710 | − | 0.979651i | \(-0.435675\pi\) |
−0.979651 | + | 0.200710i | \(0.935675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −898.046 | + | 371.983i | −1.58665 | + | 0.657213i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 788.176 | − | 788.176i | 1.38519 | − | 1.38519i | 0.550088 | − | 0.835107i | \(-0.314594\pi\) |
0.835107 | − | 0.550088i | \(-0.185406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −564.052 | − | 233.638i | −0.987832 | − | 0.409174i | −0.170511 | − | 0.985356i | \(-0.554542\pi\) |
−0.817321 | + | 0.576182i | \(0.804542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 321.332 | + | 321.332i | 0.557868 | + | 0.557868i | ||||
\(577\) | 2.00000 | 0.00346620 | 0.00173310 | − | 0.999998i | \(-0.499448\pi\) | ||||
0.00173310 | + | 0.999998i | \(0.499448\pi\) | |||||||
\(578\) | −453.879 | + | 357.879i | −0.785258 | + | 0.619168i | ||||
\(579\) | −936.592 | −1.61760 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1218.11i | − | 2.09298i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −70.3633 | + | 169.872i | −0.120485 | + | 0.290877i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 804.688 | − | 804.688i | 1.37085 | − | 1.37085i | 0.511659 | − | 0.859189i | \(-0.329031\pi\) |
0.859189 | − | 0.511659i | \(-0.170969\pi\) | |||||||
\(588\) | −726.593 | − | 300.965i | −1.23570 | − | 0.511845i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −838.294 | − | 838.294i | −1.41365 | − | 1.41365i | −0.726813 | − | 0.686836i | \(-0.758999\pi\) |
−0.686836 | − | 0.726813i | \(-0.741001\pi\) | |||||||
\(594\) | 320.670 | 0.539848 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 741.421 | − | 307.107i | 1.23570 | − | 0.511845i | ||||
\(601\) | −208.825 | + | 504.148i | −0.347462 | + | 0.838848i | 0.649456 | + | 0.760399i | \(0.274997\pi\) |
−0.996918 | + | 0.0784489i | \(0.975003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −201.633 | + | 201.633i | −0.334383 | + | 0.334383i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(608\) | 543.058i | 0.893188i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 481.998 | + | 28.4020i | 0.787579 | + | 0.0464085i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 766.504 | + | 766.504i | 1.24838 | + | 1.24838i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1132.06 | − | 468.913i | 1.83478 | − | 0.759989i | 0.872102 | − | 0.489324i | \(-0.162757\pi\) |
0.962674 | − | 0.270665i | \(-0.0872434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −89.6970 | − | 37.1537i | −0.144906 | − | 0.0600222i | 0.309052 | − | 0.951045i | \(-0.399988\pi\) |
−0.453958 | + | 0.891023i | \(0.649988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 625.000i | − | 1.00000i | ||||||
\(626\) | −272.527 | − | 657.938i | −0.435347 | − | 1.05102i | ||||
\(627\) | −1012.91 | − | 1012.91i | −1.61549 | − | 1.61549i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1668.18i | − | 2.63535i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 843.557 | − | 349.413i | 1.31600 | − | 0.545106i | 0.389372 | − | 0.921081i | \(-0.372692\pi\) |
0.926630 | + | 0.375975i | \(0.122692\pi\) | |||||||
\(642\) | 1684.55i | 2.62392i | ||||||||
\(643\) | −27.7862 | − | 67.0818i | −0.0432133 | − | 0.104326i | 0.900799 | − | 0.434236i | \(-0.142982\pi\) |
−0.944012 | + | 0.329910i | \(0.892982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 383.294 | + | 431.294i | 0.593334 | + | 0.667637i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 534.501 | + | 534.501i | 0.824848 | + | 0.824848i | ||||
\(649\) | 949.791 | + | 2293.00i | 1.46347 | + | 3.53313i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −425.553 | + | 1027.38i | −0.652689 | + | 1.57573i | ||||
\(653\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 666.843 | + | 276.215i | 1.01653 | + | 0.421060i | ||||
\(657\) | 62.4519 | − | 150.772i | 0.0950562 | − | 0.229486i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 994.000i | 1.50835i | 0.656676 | + | 0.754173i | \(0.271962\pi\) | ||||
−0.656676 | + | 0.754173i | \(0.728038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(662\) | −955.799 | −1.44381 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1181.78 | 1.77979 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.96908 | − | 2.47248i | −0.00886937 | − | 0.00367381i | 0.378244 | − | 0.925706i | \(-0.376528\pi\) |
−0.387114 | + | 0.922032i | \(0.626528\pi\) | |||||||
\(674\) | 198.821 | − | 479.997i | 0.294987 | − | 0.712162i | ||||
\(675\) | 176.041 | − | 72.9185i | 0.260801 | − | 0.108027i | ||||
\(676\) | − | 676.000i | − | 1.00000i | ||||||
\(677\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(678\) | 71.5450 | + | 71.5450i | 0.105524 | + | 0.105524i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1523.08 | 2.23653 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −520.286 | − | 1256.08i | −0.761765 | − | 1.83906i | −0.470404 | − | 0.882451i | \(-0.655892\pi\) |
−0.291362 | − | 0.956613i | \(-0.594108\pi\) | |||||||
\(684\) | − | 481.998i | − | 0.704676i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −790.823 | + | 790.823i | −1.14945 | + | 1.14945i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −306.508 | + | 739.976i | −0.443572 | + | 1.07088i | 0.531114 | + | 0.847300i | \(0.321773\pi\) |
−0.974686 | + | 0.223577i | \(0.928227\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −348.724 | − | 841.894i | −0.502484 | − | 1.21310i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 724.557 | − | 251.293i | 1.03954 | − | 0.360535i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1321.92 | + | 1321.92i | 1.89115 | + | 1.89115i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1243.84 | + | 515.216i | 1.76682 | + | 0.731841i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −484.823 | + | 484.823i | −0.686717 | + | 0.686717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −724.666 | + | 1749.50i | −1.02354 | + | 2.47104i | ||||
\(709\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −991.294 | − | 991.294i | −1.39227 | − | 1.39227i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1008.00 | − | 1008.00i | −1.40782 | − | 1.40782i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −103.238 | + | 103.238i | −0.142988 | + | 0.142988i | ||||
\(723\) | 1367.26 | − | 1367.26i | 1.89109 | − | 1.89109i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2383.87 | + | 987.431i | −3.28357 | + | 1.36010i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −279.776 | − | 279.776i | −0.383780 | − | 0.383780i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −69.8995 | + | 1186.23i | −0.0956217 | + | 1.62275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −323.293 | + | 780.499i | −0.438661 | + | 1.05902i | ||||
\(738\) | −591.865 | − | 245.159i | −0.801985 | − | 0.332193i | ||||
\(739\) | 227.688 | − | 227.688i | 0.308103 | − | 0.308103i | −0.536070 | − | 0.844173i | \(-0.680092\pi\) |
0.844173 | + | 0.536070i | \(0.180092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1048.91 | −1.40416 | ||||||||
\(748\) | 1351.49 | − | 468.729i | 1.80681 | − | 0.626643i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1710.87 | + | 708.667i | −2.27208 | + | 0.941125i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | −65.3654 | − | 27.0753i | −0.0862341 | − | 0.0357193i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 610.940i | − | 0.802812i | −0.915900 | − | 0.401406i | \(-0.868522\pi\) | ||
0.915900 | − | 0.401406i | \(-0.131478\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 393.097 | + | 949.019i | 0.511845 | + | 1.23570i | ||||
\(769\) | 1120.06i | 1.45651i | 0.685306 | + | 0.728256i | \(0.259669\pi\) | ||||
−0.685306 | + | 0.728256i | \(0.740331\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.5854 | − | 122.124i | 0.0656102 | − | 0.158397i | ||||
\(772\) | −862.593 | − | 357.298i | −1.11735 | − | 0.462821i | ||||
\(773\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(774\) | 701.905 | − | 701.905i | 0.906854 | − | 0.906854i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 464.695 | − | 1121.87i | 0.598833 | − | 1.44571i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −292.971 | − | 707.294i | −0.376085 | − | 0.907951i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −554.372 | − | 554.372i | −0.707107 | − | 0.707107i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1696.94i | 2.15896i | ||||||||
\(787\) | −1240.39 | + | 513.787i | −1.57610 | + | 0.652842i | −0.987790 | − | 0.155794i | \(-0.950207\pi\) |
−0.588310 | + | 0.808635i | \(0.700207\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1103.99 | − | 457.287i | −1.39392 | − | 0.577382i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 800.000 | 1.00000 | ||||||||
\(801\) | 879.836 | + | 879.836i | 1.09842 | + | 1.09842i | ||||
\(802\) | 472.056 | + | 1139.64i | 0.588598 | + | 1.42100i | ||||
\(803\) | − | 483.489i | − | 0.602103i | ||||||
\(804\) | −595.500 | + | 246.664i | −0.740672 | + | 0.306796i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1470.32 | − | 609.027i | −1.81746 | − | 0.752815i | −0.977750 | − | 0.209772i | \(-0.932728\pi\) |
−0.839705 | − | 0.543043i | \(-0.817272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 418.067 | − | 173.169i | 0.515496 | − | 0.213526i | −0.109741 | − | 0.993960i | \(-0.535002\pi\) |
0.625237 | + | 0.780435i | \(0.285002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 982.018 | + | 476.256i | 1.20345 | + | 0.583647i | ||||
\(817\) | 1186.23 | 1.45194 | ||||||||
\(818\) | 1080.70 | + | 1080.70i | 1.32115 | + | 1.32115i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(822\) | 416.942 | − | 1006.59i | 0.507229 | − | 1.22456i | ||||
\(823\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1492.16 | + | 1492.16i | −1.80868 | + | 1.80868i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 602.757 | − | 1455.18i | 0.728848 | − | 1.75959i | 0.0824479 | − | 0.996595i | \(-0.473726\pi\) |
0.646400 | − | 0.762999i | \(-0.276274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −831.558 | − | 49.0000i | −0.998268 | − | 0.0588235i | ||||
\(834\) | 954.033 | 1.14392 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −546.469 | − | 1319.29i | −0.653671 | − | 1.57810i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −409.453 | + | 169.601i | −0.488607 | + | 0.202388i | ||||
\(839\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 594.677 | − | 594.677i | 0.707107 | − | 0.707107i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1887.35 | + | 781.766i | 2.23885 | + | 0.927362i | ||||
\(844\) | 636.388 | − | 1536.38i | 0.754014 | − | 1.82035i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1950.17 | 2.29702 | ||||||||
\(850\) | 635.355 | − | 564.645i | 0.747477 | − | 0.664288i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −642.636 | + | 1551.46i | −0.750743 | + | 1.81245i | ||||
\(857\) | −617.969 | − | 255.971i | −0.721084 | − | 0.298683i | −0.00820166 | − | 0.999966i | \(-0.502611\pi\) |
−0.712882 | + | 0.701284i | \(0.752611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 576.927 | − | 576.927i | 0.671626 | − | 0.671626i | −0.286465 | − | 0.958091i | \(-0.592480\pi\) |
0.958091 | + | 0.286465i | \(0.0924801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 93.3356 | + | 225.332i | 0.108027 | + | 0.260801i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1289.76 | 1.48933 | ||||||||
\(867\) | 1116.06 | − | 314.875i | 1.28726 | − | 0.363177i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −412.446 | + | 995.732i | −0.472447 | + | 1.14059i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 260.844 | − | 260.844i | 0.297768 | − | 0.297768i | ||||
\(877\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −149.410 | − | 360.707i | −0.169591 | − | 0.409429i | 0.816118 | − | 0.577885i | \(-0.196122\pi\) |
−0.985709 | + | 0.168456i | \(0.946122\pi\) | |||||||
\(882\) | 492.040 | + | 492.040i | 0.557868 | + | 0.557868i | ||||
\(883\) | −1161.92 | −1.31588 | −0.657940 | − | 0.753070i | \(-0.728572\pi\) | ||||
−0.657940 | + | 0.753070i | \(0.728572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 759.206 | + | 759.206i | 0.856892 | + | 0.856892i | ||||
\(887\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1836.36 | − | 760.647i | −2.06102 | − | 0.853701i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −681.942 | − | 1646.35i | −0.759401 | − | 1.83336i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −710.051 | −0.788945 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1897.96 | −2.10417 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.5988 | + | 93.1859i | 0.0426978 | + | 0.103082i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −461.009 | + | 1112.98i | −0.508279 | + | 1.22710i | 0.436594 | + | 0.899659i | \(0.356185\pi\) |
−0.944873 | + | 0.327436i | \(0.893815\pi\) | |||||||
\(908\) | 1402.74 | + | 581.034i | 1.54487 | + | 0.639905i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(912\) | 416.942 | − | 1006.59i | 0.457173 | − | 1.10371i | ||||
\(913\) | −2871.00 | + | 1189.21i | −3.14458 | + | 1.30253i | ||||
\(914\) | − | 1764.94i | − | 1.93100i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 233.167 | + | 113.081i | 0.253995 | + | 0.123182i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −832.259 | − | 2009.25i | −0.903648 | − | 2.18160i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 150.384 | − | 363.059i | 0.161877 | − | 0.390807i | −0.822040 | − | 0.569429i | \(-0.807164\pi\) |
0.983918 | + | 0.178623i | \(0.0571642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 831.558i | 0.893188i | ||||||||
\(932\) | 713.180 | + | 1721.77i | 0.765215 | + | 1.84739i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1866.76 | 1.99867 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −507.703 | − | 507.703i | −0.541838 | − | 0.541838i | 0.382229 | − | 0.924068i | \(-0.375157\pi\) |
−0.924068 | + | 0.382229i | \(0.875157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1428.76i | 1.52158i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1334.82 | + | 1334.82i | −1.41401 | + | 1.41401i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1125.42 | − | 2717.00i | 1.18966 | − | 2.87209i | ||||
\(947\) | −278.432 | + | 115.330i | −0.294015 | + | 0.121785i | −0.524815 | − | 0.851216i | \(-0.675866\pi\) |
0.230800 | + | 0.973001i | \(0.425866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −600.000 | − | 600.000i | −0.631579 | − | 0.631579i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1243.59 | −1.30492 | −0.652461 | − | 0.757822i | \(-0.726263\pi\) | ||||
−0.652461 | + | 0.757822i | \(0.726263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −679.530 | + | 679.530i | −0.707107 | + | 0.707107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 570.380 | − | 1377.02i | 0.592295 | − | 1.42993i | ||||
\(964\) | 1780.83 | − | 737.643i | 1.84733 | − | 0.765189i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | −2572.22 | −2.65725 | ||||||||
\(969\) | −379.322 | − | 1093.71i | −0.391457 | − | 1.12870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −353.043 | − | 353.043i | −0.363587 | − | 0.363587i | 0.501545 | − | 0.865132i | \(-0.332765\pi\) |
−0.865132 | + | 0.501545i | \(0.832765\pi\) | |||||||
\(972\) | −475.352 | − | 1147.60i | −0.489045 | − | 1.18066i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1145.68 | − | 1145.68i | 1.17265 | − | 1.17265i | 0.191071 | − | 0.981576i | \(-0.438804\pi\) |
0.981576 | − | 0.191071i | \(-0.0611960\pi\) | |||||||
\(978\) | 1577.57 | − | 1577.57i | 1.61306 | − | 1.61306i | ||||
\(979\) | 3405.75 | + | 1410.71i | 3.47880 | + | 1.44097i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1187.94i | − | 1.20971i | ||||||
\(983\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(984\) | −1023.96 | − | 1023.96i | −1.04061 | − | 1.04061i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1771.62 | + | 733.831i | 1.78411 | + | 0.739004i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2190.50 | − | 907.334i | −2.19930 | − | 0.910978i | ||||
\(997\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(998\) | 446.870 | − | 185.100i | 0.447766 | − | 0.185471i | ||||
\(999\) | 0 | 0 |
(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 | 136.3.p.a.83.1 | yes | 4 | |
8.3 | odd | 2 | CM | 136.3.p.a.83.1 | yes | 4 | |
17.8 | even | 8 | inner | 136.3.p.a.59.1 | ✓ | 4 | |
136.59 | odd | 8 | inner | 136.3.p.a.59.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.p.a.59.1 | ✓ | 4 | 17.8 | even | 8 | inner | |
136.3.p.a.59.1 | ✓ | 4 | 136.59 | odd | 8 | inner | |
136.3.p.a.83.1 | yes | 4 | 1.1 | even | 1 | trivial | |
136.3.p.a.83.1 | yes | 4 | 8.3 | odd | 2 | CM |