Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(2255,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.2255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.h (of order \(2\), degree \(1\), 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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 97x^{12} - 432x^{10} + 1392x^{8} - 2502x^{6} + 3181x^{4} - 1650x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2255.9 | ||
Root | \(1.75344 + 1.01235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.2255 |
Dual form | 2352.2.h.p.2255.12 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.777403 | − | 1.54779i | 0.448834 | − | 0.893615i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.40332i | − | 1.52201i | −0.648746 | − | 0.761005i | \(-0.724706\pi\) | ||
0.648746 | − | 0.761005i | \(-0.275294\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.79129 | − | 2.40651i | −0.597096 | − | 0.802170i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.94748 | −1.09483 | −0.547417 | − | 0.836860i | \(-0.684389\pi\) | ||||
−0.547417 | + | 0.836860i | \(0.684389\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.26761 | − | 2.64575i | −1.36009 | − | 0.683130i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.09632i | 1.47858i | 0.673390 | + | 0.739288i | \(0.264838\pi\) | ||||
−0.673390 | + | 0.739288i | \(0.735162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.38774i | 1.00662i | 0.864107 | + | 0.503308i | \(0.167884\pi\) | ||||
−0.864107 | + | 0.503308i | \(0.832116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.33639 | −1.73826 | −0.869129 | − | 0.494585i | \(-0.835320\pi\) | ||||
−0.869129 | + | 0.494585i | \(0.835320\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.58258 | −1.31652 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.11732 | + | 0.901703i | −0.984828 | + | 0.173533i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.80848i | − | 0.707218i | −0.935393 | − | 0.353609i | \(-0.884954\pi\) | ||
0.935393 | − | 0.353609i | \(-0.115046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.89898i | 0.879883i | 0.898027 | + | 0.439941i | \(0.145001\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.58258 | −1.24657 | −0.623284 | − | 0.781996i | \(-0.714202\pi\) | ||||
−0.623284 | + | 0.781996i | \(0.714202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.06878 | + | 6.10985i | −0.491398 | + | 0.978359i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.710314i | − | 0.110932i | −0.998461 | − | 0.0554662i | \(-0.982335\pi\) | ||
0.998461 | − | 0.0554662i | \(-0.0176645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.66930i | − | 1.47456i | −0.675590 | − | 0.737278i | \(-0.736111\pi\) | ||
0.675590 | − | 0.737278i | \(-0.263889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.19012 | + | 6.09632i | −1.22091 | + | 0.908786i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7894 | 1.71967 | 0.859833 | − | 0.510575i | \(-0.170567\pi\) | ||||
0.859833 | + | 0.510575i | \(0.170567\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.43581 | + | 4.73930i | 1.32128 | + | 0.663635i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.00454i | − | 0.137984i | −0.997617 | − | 0.0689918i | \(-0.978022\pi\) | ||
0.997617 | − | 0.0689918i | \(-0.0219782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.79129 | + | 3.41105i | 0.899528 | + | 0.451804i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.66442 | 0.607256 | 0.303628 | − | 0.952791i | \(-0.401802\pi\) | ||||
0.303628 | + | 0.952791i | \(0.401802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.70938 | −0.218863 | −0.109432 | − | 0.993994i | \(-0.534903\pi\) | ||||
−0.109432 | + | 0.993994i | \(0.534903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.4345i | 1.66635i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.46410i | − | 0.423207i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.48074 | + | 12.9030i | −0.780189 | + | 1.55333i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.59649 | −0.782859 | −0.391429 | − | 0.920208i | \(-0.628019\pi\) | ||||
−0.391429 | + | 0.920208i | \(0.628019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3757 | −1.68255 | −0.841274 | − | 0.540609i | \(-0.818194\pi\) | ||||
−0.841274 | + | 0.540609i | \(0.818194\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.11732 | + | 10.1884i | −0.590897 | + | 1.17646i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.92820i | − | 0.779484i | −0.920924 | − | 0.389742i | \(-0.872564\pi\) | ||
0.920924 | − | 0.389742i | \(-0.127436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.58258 | + | 8.62150i | −0.286953 | + | 0.957945i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.4539 | 1.80605 | 0.903023 | − | 0.429592i | \(-0.141343\pi\) | ||||
0.903023 | + | 0.429592i | \(0.141343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.7477 | 2.25041 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.89472 | − | 2.96073i | −0.631980 | − | 0.317423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.09632i | 0.646209i | 0.946363 | + | 0.323104i | \(0.104727\pi\) | ||||
−0.946363 | + | 0.323104i | \(0.895273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.58258 | + | 3.80848i | 0.786276 | + | 0.394921i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.9329 | 1.53208 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.89949 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 11.6306i | − | 1.15729i | −0.815581 | − | 0.578643i | \(-0.803582\pi\) | ||
0.815581 | − | 0.578643i | \(-0.196418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.5734i | − | 1.83010i | −0.403345 | − | 0.915048i | \(-0.632153\pi\) | ||
0.403345 | − | 0.915048i | \(-0.367847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.59649 | 0.637706 | 0.318853 | − | 0.947804i | \(-0.396702\pi\) | ||||
0.318853 | + | 0.947804i | \(0.396702\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.41742 | −0.423113 | −0.211556 | − | 0.977366i | \(-0.567853\pi\) | ||||
−0.211556 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.89472 | + | 11.7362i | −0.559502 | + | 1.11395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.4300i | − | 1.16931i | −0.811280 | − | 0.584657i | \(-0.801229\pi\) | ||
0.811280 | − | 0.584657i | \(-0.198771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.3714i | 2.64565i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.07107 | + | 9.49964i | 0.653720 | + | 0.878242i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.09941 | − | 0.552200i | −0.0991309 | − | 0.0497902i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.38601i | 0.481739i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.9660 | − | 7.51695i | −1.31768 | − | 0.661831i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.12502 | −0.622516 | −0.311258 | − | 0.950325i | \(-0.600750\pi\) | ||||
−0.311258 | + | 0.950325i | \(0.600750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.06878 | + | 17.4159i | 0.264119 | + | 1.49892i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.2475i | 1.55899i | 0.626407 | + | 0.779496i | \(0.284525\pi\) | ||||
−0.626407 | + | 0.779496i | \(0.715475\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.511238i | − | 0.0433627i | −0.999765 | − | 0.0216813i | \(-0.993098\pi\) | ||
0.999765 | − | 0.0216813i | \(-0.00690192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.16515 | − | 18.2475i | 0.771845 | − | 1.53672i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9615 | −1.07639 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.00454i | − | 0.0822948i | −0.999153 | − | 0.0411474i | \(-0.986899\pi\) | ||
0.999153 | − | 0.0411474i | \(-0.0131013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8745i | 1.29185i | 0.763401 | + | 0.645925i | \(0.223528\pi\) | ||||
−0.763401 | + | 0.645925i | \(0.776472\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.6709 | − | 10.9203i | 1.18607 | − | 0.882851i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6728 | 1.33919 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.70938 | 0.136423 | 0.0682116 | − | 0.997671i | \(-0.478271\pi\) | ||||
0.0682116 | + | 0.997671i | \(0.478271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.55481 | − | 0.780929i | −0.123304 | − | 0.0619317i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.18710i | − | 0.327959i | −0.986464 | − | 0.163980i | \(-0.947567\pi\) | ||
0.986464 | − | 0.163980i | \(-0.0524331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.58258 | 0.198660 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5591 | − | 7.85971i | 0.807478 | − | 0.601047i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.40332i | − | 0.258750i | −0.991596 | − | 0.129375i | \(-0.958703\pi\) | ||
0.991596 | − | 0.129375i | \(-0.0412970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.62614 | − | 7.21953i | 0.272557 | − | 0.542653i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.59649 | −0.493045 | −0.246522 | − | 0.969137i | \(-0.579288\pi\) | ||||
−0.246522 | + | 0.969137i | \(0.579288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.01400 | −0.670006 | −0.335003 | − | 0.942217i | \(-0.608737\pi\) | ||||
−0.335003 | + | 0.942217i | \(0.608737\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.32888 | + | 2.64575i | −0.0982333 | + | 0.195580i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.8059i | 1.89729i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0763 | 0.729095 | 0.364548 | − | 0.931185i | \(-0.381224\pi\) | ||||
0.364548 | + | 0.931185i | \(0.381224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7477 | −1.34949 | −0.674745 | − | 0.738051i | \(-0.735747\pi\) | ||||
−0.674745 | + | 0.738051i | \(0.735747\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.7938 | + | 10.4440i | 1.48907 | + | 0.747913i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00454i | 0.0715702i | 0.999360 | + | 0.0357851i | \(0.0113932\pi\) | ||||
−0.999360 | + | 0.0357851i | \(0.988607\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.36169 | − | 2.69300i | −0.378185 | − | 0.189950i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.41742 | −0.168840 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.9329 | + | 20.0616i | 1.03791 | + | 1.39438i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8745i | 1.09285i | 0.837509 | + | 0.546423i | \(0.184011\pi\) | ||||
−0.837509 | + | 0.546423i | \(0.815989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.12813 | + | 10.2100i | −0.351374 | + | 0.699575i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.9077 | −2.24429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.1757 | + | 22.2505i | −0.755185 | + | 1.50355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 24.0651i | − | 1.61879i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.02248i | − | 0.0684701i | −0.999414 | − | 0.0342350i | \(-0.989101\pi\) | ||
0.999414 | − | 0.0342350i | \(-0.0108995\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7913 | + | 15.8410i | 0.786086 | + | 1.05607i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4539 | 1.09208 | 0.546041 | − | 0.837759i | \(-0.316134\pi\) | ||||
0.546041 | + | 0.837759i | \(0.316134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2612 | −1.00849 | −0.504244 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504244 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.2475i | − | 1.19544i | −0.801706 | − | 0.597718i | \(-0.796074\pi\) | ||
0.801706 | − | 0.597718i | \(-0.203926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 40.1232i | − | 2.61735i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.7234 | − | 5.38601i | −0.696558 | − | 0.349859i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.33639 | −0.539236 | −0.269618 | − | 0.962967i | \(-0.586898\pi\) | ||||
−0.269618 | + | 0.962967i | \(0.586898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8610 | 1.47260 | 0.736302 | − | 0.676653i | \(-0.236570\pi\) | ||||
0.736302 | + | 0.676653i | \(0.236570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3365 | + | 10.6997i | 0.727240 | + | 0.686384i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.3205i | − | 1.10208i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.7913 | − | 25.4671i | 0.810615 | − | 1.61391i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.2433 | −1.78270 | −0.891351 | − | 0.453314i | \(-0.850241\pi\) | ||||
−0.891351 | + | 0.453314i | \(0.850241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.1294 | − | 32.1131i | 1.01006 | − | 2.01100i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3236i | 0.893481i | 0.894664 | + | 0.446740i | \(0.147415\pi\) | ||||
−0.894664 | + | 0.446740i | \(0.852585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.16515 | + | 6.82209i | −0.567309 | + | 0.422277i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.7491 | −1.64942 | −0.824710 | − | 0.565556i | \(-0.808661\pi\) | ||||
−0.824710 | + | 0.565556i | \(0.808661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.41875 | −0.210012 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.43581 | + | 4.73930i | 0.577462 | + | 0.290041i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.40332i | 0.207504i | 0.994603 | + | 0.103752i | \(0.0330848\pi\) | ||||
−0.994603 | + | 0.103752i | \(0.966915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.5959i | − | 1.19037i | −0.803590 | − | 0.595184i | \(-0.797079\pi\) | ||
0.803590 | − | 0.595184i | \(-0.202921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.7894 | − | 8.77548i | 0.705815 | − | 0.525374i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.6306i | − | 0.634167i | −0.948398 | − | 0.317083i | \(-0.897296\pi\) | ||
0.948398 | − | 0.317083i | \(-0.102704\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2082i | 0.904032i | 0.892010 | + | 0.452016i | \(0.149295\pi\) | ||||
−0.892010 | + | 0.452016i | \(0.850705\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.6089 | − | 23.1129i | 0.687650 | − | 1.36909i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.1652 | −1.18619 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.69590 | + | 15.3223i | −0.451142 | + | 0.898210i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.98269i | − | 0.115830i | −0.998322 | − | 0.0579150i | \(-0.981555\pi\) | ||
0.998322 | − | 0.0579150i | \(-0.0184452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 15.8745i | − | 0.924250i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.9077 | 1.90310 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.0017 | − | 9.04165i | −1.03417 | − | 0.519429i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.81755i | 0.333112i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.511238i | 0.0291779i | 0.999894 | + | 0.0145890i | \(0.00464397\pi\) | ||||
−0.999894 | + | 0.0145890i | \(0.995356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.7477 | − | 14.4391i | −1.63540 | − | 0.821409i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.1183 | −1.19751 | −0.598754 | − | 0.800933i | \(-0.704337\pi\) | ||||
−0.598754 | + | 0.800933i | \(0.704337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0325 | 1.13231 | 0.566153 | − | 0.824300i | \(-0.308431\pi\) | ||||
0.566153 | + | 0.824300i | \(0.308431\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 27.8736i | − | 1.56554i | −0.622314 | − | 0.782768i | \(-0.713807\pi\) | ||
0.622314 | − | 0.782768i | \(-0.286193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.12813 | − | 10.2100i | 0.286224 | − | 0.569864i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.7491 | −1.48836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.9846 | 1.44136 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.43412 | + | 6.83723i | −0.189907 | + | 0.378100i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74110i | 0.150665i | 0.997158 | + | 0.0753323i | \(0.0240017\pi\) | ||||
−0.997158 | + | 0.0753323i | \(0.975998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.5826 | + | 18.2475i | 0.744321 | + | 0.999959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.7894 | −0.644126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.7477 | −1.56599 | −0.782994 | − | 0.622029i | \(-0.786309\pi\) | ||||
−0.782994 | + | 0.622029i | \(0.786309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.2390 | − | 9.66311i | −1.04492 | − | 0.524828i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 43.9129 | + | 22.0560i | 2.36419 | + | 1.18746i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.47981 | 0.186806 | 0.0934031 | − | 0.995628i | \(-0.470225\pi\) | ||||
0.0934031 | + | 0.995628i | \(0.470225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.6709 | 0.785313 | 0.392657 | − | 0.919685i | \(-0.371556\pi\) | ||||
0.392657 | + | 0.919685i | \(0.371556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.2005 | − | 3.55945i | 1.07822 | − | 0.189989i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.8683i | − | 0.897811i | −0.893579 | − | 0.448906i | \(-0.851814\pi\) | ||
0.893579 | − | 0.448906i | \(-0.148186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.4499i | 1.19152i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.33639 | 0.439978 | 0.219989 | − | 0.975502i | \(-0.429398\pi\) | ||||
0.219989 | + | 0.975502i | \(0.429398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.252273 | −0.0132775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.55144 | + | 17.0257i | −0.448834 | + | 0.893615i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.9251i | 2.56086i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.02248i | 0.0533728i | 0.999644 | + | 0.0266864i | \(0.00849556\pi\) | ||||
−0.999644 | + | 0.0266864i | \(0.991504\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70938 | + | 1.27238i | −0.0889866 | + | 0.0662373i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.33639 | + | 4.18710i | 0.430490 | + | 0.216221i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.0339i | 0.774285i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.66930i | 0.496679i | 0.968673 | + | 0.248339i | \(0.0798848\pi\) | ||||
−0.968673 | + | 0.248339i | \(0.920115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0851 | − | 8.07901i | −0.824063 | − | 0.413900i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.1183 | −1.07909 | −0.539547 | − | 0.841956i | \(-0.681404\pi\) | ||||
−0.539547 | + | 0.841956i | \(0.681404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.2693 | + | 17.3205i | −1.18284 | + | 0.880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4527i | 0.884885i | 0.896797 | + | 0.442443i | \(0.145888\pi\) | ||||
−0.896797 | + | 0.442443i | \(0.854112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 50.8213i | − | 2.57015i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.53901 | + | 11.0280i | −0.279406 | + | 0.556290i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.5789 | −1.18638 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.71846 | −0.287001 | −0.143501 | − | 0.989650i | \(-0.545836\pi\) | ||||
−0.143501 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.0696i | 1.25192i | 0.779856 | + | 0.625959i | \(0.215292\pi\) | ||||
−0.779856 | + | 0.625959i | \(0.784708\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 19.3386i | − | 0.963325i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.3417 | + | 8.78933i | 1.45800 | + | 0.436745i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.83297 | 0.238975 | 0.119487 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119487 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.2433 | + | 14.1857i | 1.39314 | + | 0.699729i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 55.9977i | − | 2.74882i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.791288 | − | 0.397438i | −0.0387495 | − | 0.0194626i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.12502 | −0.348080 | −0.174040 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174040 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4955 | −0.950150 | −0.475075 | − | 0.879945i | \(-0.657579\pi\) | ||||
−0.475075 | + | 0.879945i | \(0.657579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.1183 | − | 28.3714i | −1.02681 | − | 1.37946i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 40.1295i | − | 1.94657i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2022 | 1.84013 | 0.920066 | − | 0.391762i | \(-0.128134\pi\) | ||||
0.920066 | + | 0.391762i | \(0.128134\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1376 | 0.583296 | 0.291648 | − | 0.956526i | \(-0.405796\pi\) | ||||
0.291648 | + | 0.956526i | \(0.405796\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0763 | + | 20.0616i | −0.483122 | + | 0.961881i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 36.5779i | − | 1.74976i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.6969i | − | 0.701447i | −0.936479 | − | 0.350723i | \(-0.885936\pi\) | ||
0.936479 | − | 0.350723i | \(-0.114064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.2693 | 1.10556 | 0.552778 | − | 0.833328i | \(-0.313568\pi\) | ||||
0.552778 | + | 0.833328i | \(0.313568\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.7477 | 0.983537 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.55481 | − | 0.780929i | −0.0735398 | − | 0.0369367i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.8600i | 1.17321i | 0.809872 | + | 0.586607i | \(0.199537\pi\) | ||||
−0.809872 | + | 0.586607i | \(0.800463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.5704 | + | 12.3409i | 1.15442 | + | 0.579826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.74773 | 0.128533 | 0.0642666 | − | 0.997933i | \(-0.479529\pi\) | ||||
0.0642666 | + | 0.997933i | \(0.479529\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.49707 | − | 31.1968i | −0.256581 | − | 1.45614i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.78933i | − | 0.409360i | −0.978829 | − | 0.204680i | \(-0.934385\pi\) | ||
0.978829 | − | 0.204680i | \(-0.0656153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.48220i | − | 0.254780i | −0.991853 | − | 0.127390i | \(-0.959340\pi\) | ||
0.991853 | − | 0.127390i | \(-0.0406599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9615 | − | 25.8059i | 0.601074 | − | 1.19672i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.7827 | 1.19308 | 0.596541 | − | 0.802583i | \(-0.296541\pi\) | ||||
0.596541 | + | 0.802583i | \(0.296541\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32888 | − | 2.64575i | 0.0612314 | − | 0.121910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 28.8826i | − | 1.32523i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.41742 | + | 1.79941i | −0.110686 | + | 0.0823894i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2500 | 0.651101 | 0.325550 | − | 0.945525i | \(-0.394450\pi\) | ||||
0.325550 | + | 0.945525i | \(0.394450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.9320 | 1.36478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.6911i | 1.52984i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.91010i | − | 0.222498i | −0.993793 | − | 0.111249i | \(-0.964515\pi\) | ||
0.993793 | − | 0.111249i | \(-0.0354851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.48074 | − | 3.25507i | −0.293069 | − | 0.147199i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0763 | −0.454737 | −0.227369 | − | 0.973809i | \(-0.573012\pi\) | ||||
−0.227369 | + | 0.973809i | \(0.573012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.2177 | 1.04567 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22.8027i | − | 1.02079i | −0.859940 | − | 0.510395i | \(-0.829499\pi\) | ||
0.859940 | − | 0.510395i | \(-0.170501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.2500 | 0.635378 | 0.317689 | − | 0.948195i | \(-0.397093\pi\) | ||||
0.317689 | + | 0.948195i | \(0.397093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.5826 | −1.76140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00770 | − | 3.99728i | 0.0891652 | − | 0.177525i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.2092i | 1.29468i | 0.762203 | + | 0.647338i | \(0.224118\pi\) | ||||
−0.762203 | + | 0.647338i | \(0.775882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.95644 | − | 22.4535i | −0.174681 | − | 0.991345i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −63.2113 | −2.78542 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.26761 | − | 2.64575i | −0.231222 | − | 0.116136i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.8683i | − | 0.739015i | −0.929228 | − | 0.369508i | \(-0.879526\pi\) | ||
0.929228 | − | 0.369508i | \(-0.120474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.7591i | − | 1.43246i | −0.697866 | − | 0.716229i | \(-0.745867\pi\) | ||
0.697866 | − | 0.716229i | \(-0.254133\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.8658 | −1.30097 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.4955 | 2.02154 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.35532 | − | 11.2250i | −0.362590 | − | 0.487122i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.80395i | 0.121452i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 22.4499i | − | 0.970596i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.12813 | + | 10.2100i | −0.221295 | + | 0.440592i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4955 | 1.35410 | 0.677048 | − | 0.735939i | \(-0.263259\pi\) | ||||
0.677048 | + | 0.735939i | \(0.263259\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00752 | + | 13.9518i | −0.300721 | + | 0.598727i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.0339i | 0.643982i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9361i | 1.53652i | 0.640139 | + | 0.768259i | \(0.278877\pi\) | ||||
−0.640139 | + | 0.768259i | \(0.721123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.06199 | + | 4.11363i | 0.130682 | + | 0.175566i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7106 | 0.711897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 39.9421 | + | 20.0616i | 1.69545 | + | 0.851568i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 27.8736i | − | 1.18104i | −0.807022 | − | 0.590521i | \(-0.798922\pi\) | ||
0.807022 | − | 0.590521i | \(-0.201078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.1694i | 1.61439i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.2433 | −1.19031 | −0.595157 | − | 0.803610i | \(-0.702910\pi\) | ||||
−0.595157 | + | 0.803610i | \(0.702910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.3032 | −1.77971 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 32.6866i | − | 1.37029i | −0.728405 | − | 0.685147i | \(-0.759738\pi\) | ||
0.728405 | − | 0.685147i | \(-0.240262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.5975i | − | 0.694584i | −0.937757 | − | 0.347292i | \(-0.887101\pi\) | ||
0.937757 | − | 0.347292i | \(-0.112899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.83335 | − | 15.5960i | 0.327243 | − | 0.651531i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 54.8749 | 2.28844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.0900 | 0.877988 | 0.438994 | − | 0.898490i | \(-0.355335\pi\) | ||||
0.438994 | + | 0.898490i | \(0.355335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.5745 | + | 29.0175i | −0.605698 | + | 1.20593i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 32.3303 | − | 24.0651i | 1.33669 | − | 0.994969i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.20382 | −0.0909614 | −0.0454807 | − | 0.998965i | \(-0.514482\pi\) | ||||
−0.0454807 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.4955 | −0.885705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.55481 | + | 0.780929i | 0.0639562 | + | 0.0321231i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.7442i | 0.646537i | 0.946307 | + | 0.323269i | \(0.104782\pi\) | ||||
−0.946307 | + | 0.323269i | \(0.895218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.1652 | + | 7.61697i | 0.620668 | + | 0.311742i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7491 | 1.09294 | 0.546469 | − | 0.837479i | \(-0.315972\pi\) | ||||
0.546469 | + | 0.837479i | \(0.315972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1376 | −0.495103 | −0.247551 | − | 0.968875i | \(-0.579626\pi\) | ||||
−0.247551 | + | 0.968875i | \(0.579626\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.33639 | + | 6.20520i | −0.339484 | + | 0.252695i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 37.4365i | 1.52201i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.87650i | − | 0.157342i | −0.996901 | − | 0.0786712i | \(-0.974932\pi\) | ||
0.996901 | − | 0.0786712i | \(-0.0250677\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.5385 | −1.88275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.2432 | −1.78697 | −0.893483 | − | 0.449098i | \(-0.851745\pi\) | ||||
−0.893483 | + | 0.449098i | \(0.851745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.87931 | + | 3.74166i | −0.0757813 | + | 0.150878i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.0696i | − | 1.00927i | −0.863334 | − | 0.504633i | \(-0.831628\pi\) | ||
0.863334 | − | 0.504633i | \(-0.168372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0847i | 0.767078i | 0.923525 | + | 0.383539i | \(0.125295\pi\) | ||||
−0.923525 | + | 0.383539i | \(0.874705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 42.6600 | − | 7.51695i | 1.71189 | − | 0.301645i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5826 | −0.583303 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 46.2258i | − | 1.84314i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.37420i | − | 0.333372i | −0.986010 | − | 0.166686i | \(-0.946693\pi\) | ||
0.986010 | − | 0.166686i | \(-0.0533066\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.5704 | + | 12.3409i | 0.976584 | + | 0.490507i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.3683 | −1.40355 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8162 | + | 15.8745i | 0.467442 | + | 0.627986i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.6866i | − | 1.29104i | −0.763742 | − | 0.645521i | \(-0.776640\pi\) | ||
0.763742 | − | 0.645521i | \(-0.223360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.0397i | 0.671981i | 0.941865 | + | 0.335991i | \(0.109071\pi\) | ||||
−0.941865 | + | 0.335991i | \(0.890929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.5826 | + | 50.9341i | −1.00731 | + | 2.00553i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.46060 | 0.0967361 | 0.0483681 | − | 0.998830i | \(-0.484598\pi\) | ||||
0.0483681 | + | 0.998830i | \(0.484598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 11.4255i | − | 0.447112i | −0.974691 | − | 0.223556i | \(-0.928233\pi\) | ||
0.974691 | − | 0.223556i | \(-0.0717666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.2487i | 0.947476i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.7510 | + | 34.5952i | 1.00464 | + | 1.34969i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.5385 | 1.81288 | 0.906442 | − | 0.422330i | \(-0.138788\pi\) | ||||
0.906442 | + | 0.422330i | \(0.138788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1176 | 1.40481 | 0.702406 | − | 0.711776i | \(-0.252109\pi\) | ||||
0.702406 | + | 0.711776i | \(0.252109\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.2476 | − | 18.7083i | −1.44658 | − | 0.726570i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.7490i | 1.22933i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.58258 | − | 0.794877i | −0.0611859 | − | 0.0307317i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.16515 | 0.122008 | 0.0610038 | − | 0.998138i | \(-0.480570\pi\) | ||||
0.0610038 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.6851 | − | 5.93553i | 1.29654 | − | 0.228459i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 29.2092i | − | 1.12260i | −0.827612 | − | 0.561301i | \(-0.810301\pi\) | ||
0.827612 | − | 0.561301i | \(-0.189699\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.7913 | − | 25.4671i | 0.490163 | − | 0.975900i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.0763 | 0.385559 | 0.192779 | − | 0.981242i | \(-0.438250\pi\) | ||||
0.192779 | + | 0.981242i | \(0.438250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 62.1022 | 2.37280 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8641 | + | 23.6211i | −0.452644 | + | 0.901200i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.96538i | 0.151069i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.9837i | 0.912381i | 0.889882 | + | 0.456191i | \(0.150787\pi\) | ||||
−0.889882 | + | 0.456191i | \(0.849213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.73991 | −0.0659984 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.33030 | 0.164022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.2433 | − | 14.1857i | −1.06826 | − | 0.536552i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.6866i | − | 1.23456i | −0.786745 | − | 0.617278i | \(-0.788235\pi\) | ||
0.786745 | − | 0.617278i | \(-0.211765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 33.2704i | − | 1.25482i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −62.1022 | − | 31.1919i | −2.33890 | − | 1.17476i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0780 | −0.641379 | −0.320689 | − | 0.947184i | \(-0.603915\pi\) | ||||
−0.320689 | + | 0.947184i | \(0.603915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.6728 | + | 12.4104i | −0.625278 | + | 0.465427i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 40.8398i | − | 1.52946i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.48074 | + | 12.9030i | −0.242028 | + | 0.481870i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.46060 | −0.0917649 | −0.0458824 | − | 0.998947i | \(-0.514610\pi\) | ||||
−0.0458824 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.7722 | − | 35.3839i | 0.660955 | − | 1.31594i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.0696i | 0.931063i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.0683i | − | 1.59732i | −0.601785 | − | 0.798658i | \(-0.705544\pi\) | ||
0.601785 | − | 0.798658i | \(-0.294456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.3739 | − | 9.22860i | 0.939773 | − | 0.341800i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.9472 | 2.18024 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4993 | −0.646351 | −0.323175 | − | 0.946339i | \(-0.604750\pi\) | ||||
−0.323175 | + | 0.946339i | \(0.604750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.9717i | − | 0.918599i | −0.888281 | − | 0.459300i | \(-0.848100\pi\) | ||
0.888281 | − | 0.459300i | \(-0.151900\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.8085 | − | 13.4650i | −0.984833 | − | 0.494650i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5294 | −0.789836 | −0.394918 | − | 0.918716i | \(-0.629227\pi\) | ||||
−0.394918 | + | 0.918716i | \(0.629227\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.41875 | −0.125253 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.4736 | − | 39.5964i | −1.07838 | − | 1.44876i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.94630i | 0.326455i | 0.986588 | + | 0.163228i | \(0.0521905\pi\) | ||||
−0.986588 | + | 0.163228i | \(0.947809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.9564 | + | 43.7146i | −0.800137 | + | 1.59305i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.0260 | 1.96621 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7477 | 0.826780 | 0.413390 | − | 0.910554i | \(-0.364345\pi\) | ||||
0.413390 | + | 0.910554i | \(0.364345\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14.3236i | − | 0.519230i | −0.965712 | − | 0.259615i | \(-0.916404\pi\) | ||
0.965712 | − | 0.259615i | \(-0.0835956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.1652 | − | 49.9296i | −1.34371 | − | 1.80521i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.4127 | −0.664844 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0031 | −1.33437 | −0.667183 | − | 0.744894i | \(-0.732500\pi\) | ||||
−0.667183 | + | 0.744894i | \(0.732500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.1699 | + | 11.1352i | 0.798428 | + | 0.401025i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.40332i | − | 0.122409i | −0.998125 | − | 0.0612044i | \(-0.980506\pi\) | ||
0.998125 | − | 0.0612044i | \(-0.0194942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 32.2479i | − | 1.15838i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.11667 | 0.111666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.43412 | + | 19.4892i | 0.122725 | + | 0.696488i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.81755i | − | 0.207637i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8377i | 0.956660i | 0.878180 | + | 0.478330i | \(0.158758\pi\) | ||||
−0.878180 | + | 0.478330i | \(0.841242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.7948 | + | 41.4019i | −0.740316 | + | 1.47395i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.74773 | 0.239619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.65775 | + | 5.29150i | −0.0942607 | + | 0.187670i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 17.0166i | − | 0.602759i | −0.953504 | − | 0.301379i | \(-0.902553\pi\) | ||
0.953504 | − | 0.301379i | \(-0.0974470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 71.8722i | 2.54266i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.6709 | − | 10.9203i | 0.518369 | − | 0.385849i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.26761 | + | 2.64575i | 0.185429 | + | 0.0931349i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39.2990i | − | 1.38168i | −0.723008 | − | 0.690840i | \(-0.757241\pi\) | ||
0.723008 | − | 0.690840i | \(-0.242759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1296i | 0.741962i | 0.928641 | + | 0.370981i | \(0.120978\pi\) | ||||
−0.928641 | + | 0.370981i | \(0.879022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.3303 | − | 15.2339i | −1.06373 | − | 0.534277i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.2500 | −0.499157 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.4264 | 1.48431 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 27.8736i | − | 0.972795i | −0.873738 | − | 0.486397i | \(-0.838311\pi\) | ||
0.873738 | − | 0.486397i | \(-0.161689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.37420i | 0.291906i | 0.989291 | + | 0.145953i | \(0.0466249\pi\) | ||||
−0.989291 | + | 0.145953i | \(0.953375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0763 | 0.350387 | 0.175194 | − | 0.984534i | \(-0.443945\pi\) | ||||
0.175194 | + | 0.984534i | \(0.443945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1561 | −0.804246 | −0.402123 | − | 0.915586i | \(-0.631728\pi\) | ||||
−0.402123 | + | 0.915586i | \(0.631728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.55481 | − | 3.09557i | 0.0539357 | − | 0.107384i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.41742 | − | 25.0696i | −0.152689 | − | 0.866533i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.46060 | 0.0849493 | 0.0424747 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424747 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4955 | 0.499843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.4539 | − | 8.26424i | −0.566701 | − | 0.284636i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 8.78933i | − | 0.302362i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.5390 | + | 11.8229i | 0.807857 | + | 0.405760i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.2113 | 2.16686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7850 | −0.369271 | −0.184635 | − | 0.982807i | \(-0.559110\pi\) | ||||
−0.184635 | + | 0.982807i | \(0.559110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.7491 | − | 35.9361i | −0.914799 | − | 1.22899i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.7435i | − | 1.18682i | −0.804902 | − | 0.593408i | \(-0.797782\pi\) | ||
0.804902 | − | 0.593408i | \(-0.202218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8602i | 0.950576i | 0.879830 | + | 0.475288i | \(0.157656\pi\) | ||||
−0.879830 | + | 0.475288i | \(0.842344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.4622 | −1.24119 | −0.620595 | − | 0.784132i | \(-0.713109\pi\) | ||||
−0.620595 | + | 0.784132i | \(0.713109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5826 | −0.393819 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6765 | + | 31.2114i | −0.532400 | + | 1.05999i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6745i | 0.463341i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.7328 | + | 23.8232i | 0.600166 | + | 0.806294i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.5826 | 0.661257 | 0.330628 | − | 0.943761i | \(-0.392739\pi\) | ||||
0.330628 | + | 0.943761i | \(0.392739\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.06878 | − | 1.54135i | −0.103507 | − | 0.0519885i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1302i | 0.711895i | 0.934506 | + | 0.355948i | \(0.115842\pi\) | ||||
−0.934506 | + | 0.355948i | \(0.884158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.1413i | − | 1.41817i | −0.705124 | − | 0.709084i | \(-0.749109\pi\) | ||
0.705124 | − | 0.709084i | \(-0.250891\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.5704 | − | 12.3409i | −0.825923 | − | 0.414835i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.7290i | 1.73105i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.4499i | 0.750419i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.5826 | − | 50.9341i | 0.854177 | − | 1.70064i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.6577 | 0.622269 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.12397 | 0.204019 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.6775i | 1.01976i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.8383i | 0.393084i | 0.980495 | + | 0.196542i | \(0.0629713\pi\) | ||||
−0.980495 | + | 0.196542i | \(0.937029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.9891 | + | 20.8337i | −0.928340 | + | 0.691011i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5294 | −0.713300 | −0.356650 | − | 0.934238i | \(-0.616081\pi\) | ||||
−0.356650 | + | 0.934238i | \(0.616081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.00433 | + | 4.52259i | 0.297674 | + | 0.149512i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.0514i | 1.55208i | 0.630682 | + | 0.776042i | \(0.282775\pi\) | ||||
−0.630682 | + | 0.776042i | \(0.717225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.791288 | + | 0.397438i | 0.0260738 | + | 0.0130960i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.0395 | 0.857100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.9129 | 1.64113 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −44.6972 | + | 33.2704i | −1.46805 | + | 1.09274i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.6404i | 0.906851i | 0.891294 | + | 0.453425i | \(0.149798\pi\) | ||||
−0.891294 | + | 0.453425i | \(0.850202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.4174 | + | 32.6866i | −0.537482 | + | 1.07011i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0801 | 0.361973 | 0.180986 | − | 0.983486i | \(-0.442071\pi\) | ||||
0.180986 | + | 0.983486i | \(0.442071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.5734 | − | 31.0061i | 0.508218 | − | 1.01185i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.4372i | 0.601036i | 0.953776 | + | 0.300518i | \(0.0971596\pi\) | ||||
−0.953776 | + | 0.300518i | \(0.902840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.92146i | 0.192829i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.0184 | 1.62538 | 0.812689 | − | 0.582697i | \(-0.198003\pi\) | ||||
0.812689 | + | 0.582697i | \(0.198003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.7477 | 1.84211 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −43.1424 | − | 21.6690i | −1.39899 | − | 0.702666i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.8963i | 1.06561i | 0.846237 | + | 0.532807i | \(0.178863\pi\) | ||||
−0.846237 | + | 0.532807i | \(0.821137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 34.2929i | − | 1.10969i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.8162 | − | 15.8745i | −0.380772 | − | 0.511549i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 63.8045i | 2.05394i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.7309i | − | 0.956082i | −0.878338 | − | 0.478041i | \(-0.841347\pi\) | ||
0.878338 | − | 0.478041i | \(-0.158653\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7948 | + | 41.4019i | −0.668026 | + | 1.33002i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.20382 | −0.0707240 | −0.0353620 | − | 0.999375i | \(-0.511258\pi\) | ||||
−0.0353620 | + | 0.999375i | \(0.511258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.2005 | − | 40.2186i | 0.646933 | − | 1.28803i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 31.8917i | − | 1.02031i | −0.860084 | − | 0.510153i | \(-0.829589\pi\) | ||
0.860084 | − | 0.510153i | \(-0.170411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.91288 | + | 10.6306i | 0.252639 | + | 0.339408i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.7894 | −0.376025 | −0.188012 | − | 0.982167i | \(-0.560205\pi\) | ||||
−0.188012 | + | 0.982167i | \(0.560205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.41875 | 0.108931 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 80.6071i | 2.56316i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.03620i | 0.128214i | 0.997943 | + | 0.0641071i | \(0.0204199\pi\) | ||||
−0.997943 | + | 0.0641071i | \(0.979580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.24264 | + | 2.13094i | 0.134636 | + | 0.0676234i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.3456 | 1.05713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.6603 | −1.44608 | −0.723039 | − | 0.690807i | \(-0.757255\pi\) | ||||
−0.723039 | + | 0.690807i | \(0.757255\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.8024 | − | 6.83723i | 1.22765 | − | 0.216320i |
(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 | 2352.2.h.p.2255.9 | yes | 16 | |
3.2 | odd | 2 | inner | 2352.2.h.p.2255.6 | yes | 16 | |
4.3 | odd | 2 | inner | 2352.2.h.p.2255.7 | yes | 16 | |
7.6 | odd | 2 | inner | 2352.2.h.p.2255.8 | yes | 16 | |
12.11 | even | 2 | inner | 2352.2.h.p.2255.12 | yes | 16 | |
21.20 | even | 2 | inner | 2352.2.h.p.2255.11 | yes | 16 | |
28.27 | even | 2 | inner | 2352.2.h.p.2255.10 | yes | 16 | |
84.83 | odd | 2 | inner | 2352.2.h.p.2255.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.h.p.2255.5 | ✓ | 16 | 84.83 | odd | 2 | inner | |
2352.2.h.p.2255.6 | yes | 16 | 3.2 | odd | 2 | inner | |
2352.2.h.p.2255.7 | yes | 16 | 4.3 | odd | 2 | inner | |
2352.2.h.p.2255.8 | yes | 16 | 7.6 | odd | 2 | inner | |
2352.2.h.p.2255.9 | yes | 16 | 1.1 | even | 1 | trivial | |
2352.2.h.p.2255.10 | yes | 16 | 28.27 | even | 2 | inner | |
2352.2.h.p.2255.11 | yes | 16 | 21.20 | even | 2 | inner | |
2352.2.h.p.2255.12 | yes | 16 | 12.11 | even | 2 | inner |