Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1057 |
Dual form | 1200.3.bg.e.193.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.550510 | − | 0.550510i | −0.0786443 | − | 0.0786443i | 0.666690 | − | 0.745335i | \(-0.267710\pi\) |
−0.745335 | + | 0.666690i | \(0.767710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.55051 | 0.140955 | 0.0704777 | − | 0.997513i | \(-0.477548\pi\) | ||||
0.0704777 | + | 0.997513i | \(0.477548\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.55051 | + | 9.55051i | −0.734655 | + | 0.734655i | −0.971538 | − | 0.236883i | \(-0.923874\pi\) |
0.236883 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.1464 | − | 11.1464i | −0.655672 | − | 0.655672i | 0.298681 | − | 0.954353i | \(-0.403453\pi\) |
−0.954353 | + | 0.298681i | \(0.903453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.6969i | 0.668260i | 0.942527 | + | 0.334130i | \(0.108442\pi\) | ||||
−0.942527 | + | 0.334130i | \(0.891558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34847 | −0.0642128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −21.3485 | + | 21.3485i | −0.928194 | + | 0.928194i | −0.997589 | − | 0.0693950i | \(-0.977893\pi\) |
0.0693950 | + | 0.997589i | \(0.477893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 44.0454i | 1.51881i | 0.650620 | + | 0.759404i | \(0.274509\pi\) | ||||
−0.650620 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.4949 | 1.43532 | 0.717660 | − | 0.696394i | \(-0.245213\pi\) | ||||
0.717660 | + | 0.696394i | \(0.245213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.89898 | − | 1.89898i | 0.0575448 | − | 0.0575448i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.6515 | − | 20.6515i | −0.558149 | − | 0.558149i | 0.370631 | − | 0.928780i | \(-0.379142\pi\) |
−0.928780 | + | 0.370631i | \(0.879142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 23.3939i | 0.599843i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.2929 | −1.17787 | −0.588937 | − | 0.808179i | \(-0.700454\pi\) | ||||
−0.588937 | + | 0.808179i | \(0.700454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −36.2929 | + | 36.2929i | −0.844020 | + | 0.844020i | −0.989379 | − | 0.145359i | \(-0.953566\pi\) |
0.145359 | + | 0.989379i | \(0.453566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.5403 | + | 42.5403i | 0.905113 | + | 0.905113i | 0.995873 | − | 0.0907599i | \(-0.0289296\pi\) |
−0.0907599 | + | 0.995873i | \(0.528930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 48.3939i | − | 0.987630i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.3031 | −0.535354 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.4949 | − | 54.4949i | 1.02821 | − | 1.02821i | 0.0286151 | − | 0.999591i | \(-0.490890\pi\) |
0.999591 | − | 0.0286151i | \(-0.00910972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.5505 | + | 15.5505i | 0.272816 | + | 0.272816i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 47.4393i | 0.804056i | 0.915627 | + | 0.402028i | \(0.131694\pi\) | ||||
−0.915627 | + | 0.402028i | \(0.868306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −59.8888 | −0.981783 | −0.490892 | − | 0.871221i | \(-0.663329\pi\) | ||||
−0.490892 | + | 0.871221i | \(0.663329\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.65153 | + | 1.65153i | −0.0262148 | + | 0.0262148i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 81.2827 | + | 81.2827i | 1.21317 | + | 1.21317i | 0.969977 | + | 0.243197i | \(0.0781961\pi\) |
0.243197 | + | 0.969977i | \(0.421804\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 52.2929i | 0.757867i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −87.5959 | −1.23375 | −0.616873 | − | 0.787063i | \(-0.711601\pi\) | ||||
−0.616873 | + | 0.787063i | \(0.711601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −75.9898 | + | 75.9898i | −1.04096 | + | 1.04096i | −0.0418314 | + | 0.999125i | \(0.513319\pi\) |
−0.999125 | + | 0.0418314i | \(0.986681\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.853572 | − | 0.853572i | −0.0110853 | − | 0.0110853i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 97.3031i | 1.23168i | 0.787870 | + | 0.615842i | \(0.211184\pi\) | ||||
−0.787870 | + | 0.615842i | \(0.788816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 41.0556 | − | 41.0556i | 0.494646 | − | 0.494646i | −0.415120 | − | 0.909766i | \(-0.636261\pi\) |
0.909766 | + | 0.415120i | \(0.136261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 53.9444 | + | 53.9444i | 0.620050 | + | 0.620050i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 52.2020i | − | 0.586540i | −0.956030 | − | 0.293270i | \(-0.905257\pi\) | ||
0.956030 | − | 0.293270i | \(-0.0947435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5153 | 0.115553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 54.4949 | − | 54.4949i | 0.585967 | − | 0.585967i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 37.0000 | + | 37.0000i | 0.381443 | + | 0.381443i | 0.871622 | − | 0.490179i | \(-0.163068\pi\) |
−0.490179 | + | 0.871622i | \(0.663068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.65153i | − | 0.0469852i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.3383 | −0.181567 | −0.0907835 | − | 0.995871i | \(-0.528937\pi\) | ||||
−0.0907835 | + | 0.995871i | \(0.528937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6413 | + | 10.6413i | −0.103314 | + | 0.103314i | −0.756874 | − | 0.653560i | \(-0.773275\pi\) |
0.653560 | + | 0.756874i | \(0.273275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −66.9444 | − | 66.9444i | −0.625648 | − | 0.625648i | 0.321322 | − | 0.946970i | \(-0.395873\pi\) |
−0.946970 | + | 0.321322i | \(0.895873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 97.2827i | 0.892501i | 0.894908 | + | 0.446251i | \(0.147241\pi\) | ||||
−0.894908 | + | 0.446251i | \(0.852759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −50.5857 | −0.455727 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −30.1362 | + | 30.1362i | −0.266692 | + | 0.266692i | −0.827766 | − | 0.561074i | \(-0.810388\pi\) |
0.561074 | + | 0.827766i | \(0.310388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28.6515 | + | 28.6515i | 0.244885 | + | 0.244885i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2724i | 0.103130i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −118.596 | −0.980132 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −59.1464 | + | 59.1464i | −0.480865 | + | 0.480865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 66.0556 | + | 66.0556i | 0.520123 | + | 0.520123i | 0.917608 | − | 0.397486i | \(-0.130117\pi\) |
−0.397486 | + | 0.917608i | \(0.630117\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 88.8990i | 0.689139i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −86.8536 | −0.663004 | −0.331502 | − | 0.943454i | \(-0.607555\pi\) | ||||
−0.331502 | + | 0.943454i | \(0.607555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.98979 | − | 6.98979i | 0.0525548 | − | 0.0525548i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 71.5301 | + | 71.5301i | 0.522118 | + | 0.522118i | 0.918210 | − | 0.396093i | \(-0.129634\pi\) |
−0.396093 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 23.2122i | − | 0.166995i | −0.996508 | − | 0.0834973i | \(-0.973391\pi\) | ||
0.996508 | − | 0.0834973i | \(-0.0266090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 104.202 | 0.739022 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.8082 | + | 14.8082i | −0.103554 | + | 0.103554i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −59.2702 | − | 59.2702i | −0.403198 | − | 0.403198i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 137.530i | 0.923021i | 0.887135 | + | 0.461510i | \(0.152692\pi\) | ||||
−0.887135 | + | 0.461510i | \(0.847308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 291.394 | 1.92976 | 0.964880 | − | 0.262690i | \(-0.0846095\pi\) | ||||
0.964880 | + | 0.262690i | \(0.0846095\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.4393 | + | 33.4393i | −0.218557 | + | 0.218557i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 52.6311 | + | 52.6311i | 0.335230 | + | 0.335230i | 0.854569 | − | 0.519339i | \(-0.173822\pi\) |
−0.519339 | + | 0.854569i | \(0.673822\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 133.485i | − | 0.839526i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.5051 | 0.145994 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 117.576 | − | 117.576i | 0.721322 | − | 0.721322i | −0.247552 | − | 0.968875i | \(-0.579626\pi\) |
0.968875 | + | 0.247552i | \(0.0796262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −146.338 | − | 146.338i | −0.876277 | − | 0.876277i | 0.116870 | − | 0.993147i | \(-0.462714\pi\) |
−0.993147 | + | 0.116870i | \(0.962714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.4245i | − | 0.0794349i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 38.0908 | 0.222753 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.75255 | + | 3.75255i | −0.0216910 | + | 0.0216910i | −0.717869 | − | 0.696178i | \(-0.754882\pi\) |
0.696178 | + | 0.717869i | \(0.254882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 58.1010 | + | 58.1010i | 0.328254 | + | 0.328254i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 77.2372i | − | 0.431493i | −0.976449 | − | 0.215746i | \(-0.930782\pi\) | ||
0.976449 | − | 0.215746i | \(-0.0692185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 160.656 | 0.887603 | 0.443801 | − | 0.896125i | \(-0.353630\pi\) | ||||
0.443801 | + | 0.896125i | \(0.353630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −73.3485 | + | 73.3485i | −0.400811 | + | 0.400811i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.2827 | − | 17.2827i | −0.0924206 | − | 0.0924206i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.04541i | 0.0214043i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −251.868 | −1.31868 | −0.659341 | − | 0.751844i | \(-0.729165\pi\) | ||||
−0.659341 | + | 0.751844i | \(0.729165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −173.384 | + | 173.384i | −0.898361 | + | 0.898361i | −0.995291 | − | 0.0969302i | \(-0.969098\pi\) |
0.0969302 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.09082 | + | 2.09082i | 0.0106133 | + | 0.0106133i | 0.712394 | − | 0.701780i | \(-0.247611\pi\) |
−0.701780 | + | 0.712394i | \(0.747611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 304.565i | 1.53048i | 0.643746 | + | 0.765239i | \(0.277379\pi\) | ||||
−0.643746 | + | 0.765239i | \(0.722621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 199.101 | 0.990552 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.2474 | − | 24.2474i | 0.119446 | − | 0.119446i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.0454 | + | 64.0454i | 0.309398 | + | 0.309398i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.6867i | 0.0941949i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −273.151 | −1.29455 | −0.647277 | − | 0.762255i | \(-0.724092\pi\) | ||||
−0.647277 | + | 0.762255i | \(0.724092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −107.283 | + | 107.283i | −0.503674 | + | 0.503674i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.4949 | − | 24.4949i | −0.112880 | − | 0.112880i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 186.136i | 0.849937i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 212.908 | 0.963385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 174.662 | − | 174.662i | 0.783236 | − | 0.783236i | −0.197139 | − | 0.980376i | \(-0.563165\pi\) |
0.980376 | + | 0.197139i | \(0.0631650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −77.6163 | − | 77.6163i | −0.341922 | − | 0.341922i | 0.515167 | − | 0.857090i | \(-0.327730\pi\) |
−0.857090 | + | 0.515167i | \(0.827730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.96938i | 0.0391676i | 0.999808 | + | 0.0195838i | \(0.00623412\pi\) | ||||
−0.999808 | + | 0.0195838i | \(0.993766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.09082 | −0.00905115 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 50.4699 | − | 50.4699i | 0.216609 | − | 0.216609i | −0.590459 | − | 0.807068i | \(-0.701053\pi\) |
0.807068 | + | 0.590459i | \(0.201053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 119.171 | + | 119.171i | 0.502833 | + | 0.502833i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 279.737i | − | 1.17045i | −0.810872 | − | 0.585223i | \(-0.801007\pi\) | ||
0.810872 | − | 0.585223i | \(-0.198993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −397.131 | −1.64784 | −0.823922 | − | 0.566703i | \(-0.808219\pi\) | ||||
−0.823922 | + | 0.566703i | \(0.808219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −121.262 | − | 121.262i | −0.490940 | − | 0.490940i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 100.565i | − | 0.403877i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −53.8638 | −0.214597 | −0.107298 | − | 0.994227i | \(-0.534220\pi\) | ||||
−0.107298 | + | 0.994227i | \(0.534220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.1010 | + | 33.1010i | −0.130834 | + | 0.130834i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −309.732 | − | 309.732i | −1.20518 | − | 1.20518i | −0.972569 | − | 0.232614i | \(-0.925272\pi\) |
−0.232614 | − | 0.972569i | \(-0.574728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.7378i | 0.0877906i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 132.136 | 0.506269 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −128.854 | + | 128.854i | −0.489938 | + | 0.489938i | −0.908286 | − | 0.418349i | \(-0.862609\pi\) |
0.418349 | + | 0.908286i | \(0.362609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −63.9342 | − | 63.9342i | −0.239454 | − | 0.239454i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 112.227i | − | 0.417201i | −0.978001 | − | 0.208600i | \(-0.933109\pi\) | ||
0.978001 | − | 0.208600i | \(-0.0668908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −167.616 | −0.618510 | −0.309255 | − | 0.950979i | \(-0.600080\pi\) | ||||
−0.309255 | + | 0.950979i | \(0.600080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8786 | − | 12.8786i | 0.0471742 | − | 0.0471742i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 298.136 | + | 298.136i | 1.07630 | + | 1.07630i | 0.996838 | + | 0.0794665i | \(0.0253217\pi\) |
0.0794665 | + | 0.996838i | \(0.474678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 133.485i | − | 0.478440i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −336.434 | −1.19727 | −0.598636 | − | 0.801021i | \(-0.704291\pi\) | ||||
−0.598636 | + | 0.801021i | \(0.704291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1612 | − | 20.1612i | 0.0712411 | − | 0.0712411i | −0.670588 | − | 0.741830i | \(-0.733958\pi\) |
0.741830 | + | 0.670588i | \(0.233958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.5857 | + | 26.5857i | 0.0926331 | + | 0.0926331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 40.5143i | − | 0.140188i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 90.6311 | 0.311447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 246.586 | − | 246.586i | 0.841589 | − | 0.841589i | −0.147476 | − | 0.989066i | \(-0.547115\pi\) |
0.989066 | + | 0.147476i | \(0.0471150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.69694 | − | 5.69694i | −0.0191816 | − | 0.0191816i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 407.778i | − | 1.36380i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.9592 | 0.132755 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.4597 | + | 22.4597i | −0.0741244 | + | 0.0741244i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 365.373 | + | 365.373i | 1.19014 | + | 1.19014i | 0.977027 | + | 0.213114i | \(0.0683607\pi\) |
0.213114 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.0658i | 0.0843554i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 154.384 | 0.496411 | 0.248205 | − | 0.968707i | \(-0.420159\pi\) | ||||
0.248205 | + | 0.968707i | \(0.420159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 258.959 | − | 258.959i | 0.827346 | − | 0.827346i | −0.159803 | − | 0.987149i | \(-0.551086\pi\) |
0.987149 | + | 0.159803i | \(0.0510860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.85357 | + | 2.85357i | 0.00900180 | + | 0.00900180i | 0.711593 | − | 0.702592i | \(-0.247974\pi\) |
−0.702592 | + | 0.711593i | \(0.747974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 68.2929i | 0.214084i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −163.980 | −0.510840 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 141.526 | − | 141.526i | 0.438159 | − | 0.438159i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 119.146 | + | 119.146i | 0.364362 | + | 0.364362i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 46.8377i | − | 0.142364i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 497.646 | 1.50346 | 0.751731 | − | 0.659470i | \(-0.229219\pi\) | ||||
0.751731 | + | 0.659470i | \(0.229219\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −61.9546 | + | 61.9546i | −0.186050 | + | 0.186050i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −274.757 | − | 274.757i | −0.815303 | − | 0.815303i | 0.170120 | − | 0.985423i | \(-0.445584\pi\) |
−0.985423 | + | 0.170120i | \(0.945584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 73.8184i | 0.217753i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 68.9898 | 0.202316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −53.6163 | + | 53.6163i | −0.156316 | + | 0.156316i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −465.848 | − | 465.848i | −1.34250 | − | 1.34250i | −0.893563 | − | 0.448939i | \(-0.851802\pi\) |
−0.448939 | − | 0.893563i | \(-0.648198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 74.7173i | − | 0.214090i | −0.994254 | − | 0.107045i | \(-0.965861\pi\) | ||
0.994254 | − | 0.107045i | \(-0.0341389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 70.1816 | 0.199948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.8332 | − | 34.8332i | 0.0986775 | − | 0.0986775i | −0.656045 | − | 0.754722i | \(-0.727772\pi\) |
0.754722 | + | 0.656045i | \(0.227772\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.0306 | + | 15.0306i | 0.0421026 | + | 0.0421026i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 129.889i | 0.361807i | 0.983501 | + | 0.180904i | \(0.0579022\pi\) | ||||
−0.983501 | + | 0.180904i | \(0.942098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 199.788 | 0.553429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −145.250 | + | 145.250i | −0.400137 | + | 0.400137i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −160.056 | − | 160.056i | −0.436119 | − | 0.436119i | 0.454585 | − | 0.890704i | \(-0.349788\pi\) |
−0.890704 | + | 0.454585i | \(0.849788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 144.879i | 0.392625i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60.0000 | −0.161725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0250 | − | 30.0250i | 0.0804960 | − | 0.0804960i | −0.665712 | − | 0.746208i | \(-0.731872\pi\) |
0.746208 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −420.656 | − | 420.656i | −1.11580 | − | 1.11580i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 424.343i | − | 1.11964i | −0.828615 | − | 0.559819i | \(-0.810871\pi\) | ||
0.828615 | − | 0.559819i | \(-0.189129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 161.803 | 0.424679 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 325.460 | − | 325.460i | 0.849764 | − | 0.849764i | −0.140339 | − | 0.990103i | \(-0.544819\pi\) |
0.990103 | + | 0.140339i | \(0.0448193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 108.879 | + | 108.879i | 0.281340 | + | 0.281340i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 698.116i | − | 1.79464i | −0.441378 | − | 0.897321i | \(-0.645510\pi\) | ||
0.441378 | − | 0.897321i | \(-0.354490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 475.918 | 1.21718 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −106.373 | + | 106.373i | −0.270670 | + | 0.270670i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −257.984 | − | 257.984i | −0.649834 | − | 0.649834i | 0.303119 | − | 0.952953i | \(-0.401972\pi\) |
−0.952953 | + | 0.303119i | \(0.901972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 17.1214i | − | 0.0429109i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −357.151 | −0.890651 | −0.445325 | − | 0.895369i | \(-0.646912\pi\) | ||||
−0.445325 | + | 0.895369i | \(0.646912\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −424.949 | + | 424.949i | −1.05446 | + | 1.05446i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.0204 | − | 32.0204i | −0.0786742 | − | 0.0786742i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 66.3837i | − | 0.162307i | −0.996702 | − | 0.0811536i | \(-0.974140\pi\) | ||
0.996702 | − | 0.0811536i | \(-0.0258604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 175.212 | 0.426307 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.1158 | − | 26.1158i | 0.0632344 | − | 0.0632344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.4291 | − | 28.4291i | −0.0681753 | − | 0.0681753i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 414.772i | 0.989909i | 0.868919 | + | 0.494955i | \(0.164815\pi\) | ||||
−0.868919 | + | 0.494955i | \(0.835185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 762.727 | 1.81170 | 0.905851 | − | 0.423597i | \(-0.139233\pi\) | ||||
0.905851 | + | 0.423597i | \(0.139233\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 127.621 | − | 127.621i | 0.301704 | − | 0.301704i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.9694 | + | 32.9694i | 0.0772117 | + | 0.0772117i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.2724i | 0.0845512i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.3439 | −0.0495218 | −0.0247609 | − | 0.999693i | \(-0.507882\pi\) | ||||
−0.0247609 | + | 0.999693i | \(0.507882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −288.868 | + | 288.868i | −0.667132 | + | 0.667132i | −0.957051 | − | 0.289919i | \(-0.906372\pi\) |
0.289919 | + | 0.957051i | \(0.406372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −271.060 | − | 271.060i | −0.620275 | − | 0.620275i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 410.182i | − | 0.934355i | −0.884164 | − | 0.467177i | \(-0.845271\pi\) | ||
0.884164 | − | 0.467177i | \(-0.154729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.182 | −0.329210 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 262.747 | − | 262.747i | 0.593108 | − | 0.593108i | −0.345362 | − | 0.938470i | \(-0.612244\pi\) |
0.938470 | + | 0.345362i | \(0.112244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 168.439 | + | 168.439i | 0.376822 | + | 0.376822i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 841.242i | − | 1.87359i | −0.349879 | − | 0.936795i | \(-0.613777\pi\) | ||
0.349879 | − | 0.936795i | \(-0.386223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74.8786 | −0.166028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 356.883 | − | 356.883i | 0.787822 | − | 0.787822i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8286 | + | 23.8286i | 0.0521413 | + | 0.0521413i | 0.732697 | − | 0.680555i | \(-0.238261\pi\) |
−0.680555 | + | 0.732697i | \(0.738261\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 81.9092i | 0.178451i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 44.3179 | 0.0961342 | 0.0480671 | − | 0.998844i | \(-0.484694\pi\) | ||||
0.0480671 | + | 0.998844i | \(0.484694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −193.116 | + | 193.116i | −0.417097 | + | 0.417097i | −0.884202 | − | 0.467105i | \(-0.845297\pi\) |
0.467105 | + | 0.884202i | \(0.345297\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 377.369 | + | 377.369i | 0.808070 | + | 0.808070i | 0.984342 | − | 0.176271i | \(-0.0564036\pi\) |
−0.176271 | + | 0.984342i | \(0.556404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 89.4939i | − | 0.190818i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 128.919 | 0.273714 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −56.2724 | + | 56.2724i | −0.118969 | + | 0.118969i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −163.485 | − | 163.485i | −0.342735 | − | 0.342735i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 112.141i | − | 0.234114i | −0.993125 | − | 0.117057i | \(-0.962654\pi\) | ||
0.993125 | − | 0.117057i | \(-0.0373461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 394.465 | 0.820094 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.7878 | − | 28.7878i | 0.0596020 | − | 0.0596020i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.9444 | − | 41.9444i | −0.0861281 | − | 0.0861281i | 0.662730 | − | 0.748858i | \(-0.269398\pi\) |
−0.748858 | + | 0.662730i | \(0.769398\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 288.000i | − | 0.588957i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 926.468 | 1.88690 | 0.943450 | − | 0.331515i | \(-0.107560\pi\) | ||||
0.943450 | + | 0.331515i | \(0.107560\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 490.949 | − | 490.949i | 0.995840 | − | 0.995840i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 48.2225 | + | 48.2225i | 0.0970271 | + | 0.0970271i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 67.5255i | − | 0.135322i | −0.997708 | − | 0.0676608i | \(-0.978446\pi\) | ||
0.997708 | − | 0.0676608i | \(-0.0215536\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −358.454 | −0.715477 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −180.470 | + | 180.470i | −0.358787 | + | 0.358787i | −0.863366 | − | 0.504579i | \(-0.831648\pi\) |
0.504579 | + | 0.863366i | \(0.331648\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.4416 | − | 16.4416i | −0.0324291 | − | 0.0324291i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 920.772i | 1.80898i | 0.426493 | + | 0.904491i | \(0.359749\pi\) | ||||
−0.426493 | + | 0.904491i | \(0.640251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 83.6663 | 0.163731 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46.6515 | − | 46.6515i | 0.0909387 | − | 0.0909387i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 65.9592 | + | 65.9592i | 0.127581 | + | 0.127581i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.19184i | 0.0177107i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −333.687 | −0.640474 | −0.320237 | − | 0.947338i | \(-0.603762\pi\) | ||||
−0.320237 | + | 0.947338i | \(0.603762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −380.474 | + | 380.474i | −0.727485 | + | 0.727485i | −0.970118 | − | 0.242633i | \(-0.921989\pi\) |
0.242633 | + | 0.970118i | \(0.421989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −495.959 | − | 495.959i | −0.941099 | − | 0.941099i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 382.514i | − | 0.723089i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 142.318 | 0.268019 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 461.221 | − | 461.221i | 0.865331 | − | 0.865331i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −94.5959 | − | 94.5959i | −0.176156 | − | 0.176156i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 75.0352i | − | 0.139212i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 156.515 | 0.289307 | 0.144654 | − | 0.989482i | \(-0.453793\pi\) | ||||
0.144654 | + | 0.989482i | \(0.453793\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 196.763 | − | 196.763i | 0.362362 | − | 0.362362i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6061 | − | 12.6061i | −0.0230459 | − | 0.0230459i | 0.695490 | − | 0.718536i | \(-0.255187\pi\) |
−0.718536 | + | 0.695490i | \(0.755187\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 179.666i | 0.327261i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −559.242 | −1.01496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 53.5663 | − | 53.5663i | 0.0968650 | − | 0.0968650i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0194 | + | 21.0194i | 0.0377368 | + | 0.0377368i | 0.725723 | − | 0.687987i | \(-0.241505\pi\) |
−0.687987 | + | 0.725723i | \(0.741505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 693.231i | − | 1.24013i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.3337 | −0.0754611 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 360.536 | − | 360.536i | 0.640383 | − | 0.640383i | −0.310266 | − | 0.950650i | \(-0.600418\pi\) |
0.950650 | + | 0.310266i | \(0.100418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.95459 | + | 4.95459i | 0.00873826 | + | 0.00873826i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 486.504i | − | 0.855016i | −0.904012 | − | 0.427508i | \(-0.859392\pi\) | ||
0.904012 | − | 0.427508i | \(-0.140608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −447.040 | −0.782907 | −0.391453 | − | 0.920198i | \(-0.628028\pi\) | ||||
−0.391453 | + | 0.920198i | \(0.628028\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −308.474 | + | 308.474i | −0.538350 | + | 0.538350i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 248.444 | + | 248.444i | 0.430579 | + | 0.430579i | 0.888825 | − | 0.458247i | \(-0.151522\pi\) |
−0.458247 | + | 0.888825i | \(0.651522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 424.702i | 0.733509i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.2031 | −0.0778022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 84.4949 | − | 84.4949i | 0.144931 | − | 0.144931i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 547.712 | + | 547.712i | 0.933069 | + | 0.933069i | 0.997897 | − | 0.0648271i | \(-0.0206496\pi\) |
−0.0648271 | + | 0.997897i | \(0.520650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 564.949i | 0.959166i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.12143 | 0.00866570 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 78.9444 | − | 78.9444i | 0.133127 | − | 0.133127i | −0.637403 | − | 0.770530i | \(-0.719991\pi\) |
0.770530 | + | 0.637403i | \(0.219991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 373.015 | + | 373.015i | 0.624815 | + | 0.624815i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 381.807i | 0.637408i | 0.947854 | + | 0.318704i | \(0.103248\pi\) | ||||
−0.947854 | + | 0.318704i | \(0.896752\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −231.757 | −0.385619 | −0.192810 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192810 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 243.848 | − | 243.848i | 0.404391 | − | 0.404391i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 96.8434 | + | 96.8434i | 0.159544 | + | 0.159544i | 0.782365 | − | 0.622821i | \(-0.214013\pi\) |
−0.622821 | + | 0.782365i | \(0.714013\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 59.3939i | − | 0.0975269i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −812.563 | −1.32989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −105.712 | + | 105.712i | −0.172450 | + | 0.172450i | −0.788055 | − | 0.615605i | \(-0.788912\pi\) |
0.615605 | + | 0.788055i | \(0.288912\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.9250 | + | 41.9250i | 0.0679498 | + | 0.0679498i | 0.740265 | − | 0.672315i | \(-0.234700\pi\) |
−0.672315 | + | 0.740265i | \(0.734700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 434.363i | 0.701718i | 0.936428 | + | 0.350859i | \(0.114110\pi\) | ||||
−0.936428 | + | 0.350859i | \(0.885890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 156.879 | 0.252622 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.7378 | + | 28.7378i | −0.0461280 | + | 0.0461280i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.1112 | + | 24.1112i | 0.0384549 | + | 0.0384549i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 460.382i | 0.731926i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −816.413 | −1.29384 | −0.646920 | − | 0.762558i | \(-0.723943\pi\) | ||||
−0.646920 | + | 0.762558i | \(0.723943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −334.540 | + | 334.540i | −0.528500 | + | 0.528500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 462.186 | + | 462.186i | 0.725567 | + | 0.725567i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 262.788i | 0.411248i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −937.959 | −1.46327 | −0.731637 | − | 0.681694i | \(-0.761244\pi\) | ||||
−0.731637 | + | 0.681694i | \(0.761244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 62.8786 | − | 62.8786i | 0.0977894 | − | 0.0977894i | −0.656520 | − | 0.754309i | \(-0.727972\pi\) |
0.754309 | + | 0.656520i | \(0.227972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −86.3087 | − | 86.3087i | −0.133398 | − | 0.133398i | 0.637255 | − | 0.770653i | \(-0.280070\pi\) |
−0.770653 | + | 0.637255i | \(0.780070\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 73.5551i | 0.113336i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −60.0000 | −0.0921659 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −294.904 | + | 294.904i | −0.451613 | + | 0.451613i | −0.895890 | − | 0.444276i | \(-0.853461\pi\) |
0.444276 | + | 0.895890i | \(0.353461\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 227.969 | + | 227.969i | 0.346985 | + | 0.346985i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1156.80i | − | 1.75539i | −0.479220 | − | 0.877695i | \(-0.659081\pi\) | ||
0.479220 | − | 0.877695i | \(-0.340919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 908.838 | 1.37494 | 0.687472 | − | 0.726211i | \(-0.258720\pi\) | ||||
0.687472 | + | 0.726211i | \(0.258720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 260.758 | − | 260.758i | 0.393300 | − | 0.393300i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −940.302 | − | 940.302i | −1.40975 | − | 1.40975i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 427.832i | − | 0.639510i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −92.8582 | −0.138388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −833.756 | + | 833.756i | −1.23886 | + | 1.23886i | −0.278400 | + | 0.960465i | \(0.589804\pi\) |
−0.960465 | + | 0.278400i | \(0.910196\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 200.257 | + | 200.257i | 0.295800 | + | 0.295800i | 0.839366 | − | 0.543566i | \(-0.182926\pi\) |
−0.543566 | + | 0.839366i | \(0.682926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 40.7378i | − | 0.0599967i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −190.120 | −0.279178 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 156.025 | − | 156.025i | 0.228441 | − | 0.228441i | −0.583600 | − | 0.812041i | \(-0.698357\pi\) |
0.812041 | + | 0.583600i | \(0.198357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9852 | + | 10.9852i | 0.0159901 | + | 0.0159901i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1040.91i | 1.51075i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −774.940 | −1.12148 | −0.560738 | − | 0.827993i | \(-0.689482\pi\) | ||||
−0.560738 | + | 0.827993i | \(0.689482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.56072 | + | 2.56072i | −0.00369512 | + | 0.00369512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 538.293 | + | 538.293i | 0.772300 | + | 0.772300i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 123.626i | − | 0.176861i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 280.309 | 0.399870 | 0.199935 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199935 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 262.211 | − | 262.211i | 0.372989 | − | 0.372989i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0954 | + | 10.0954i | 0.0142792 | + | 0.0142792i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 926.686i | 1.30703i | 0.756913 | + | 0.653516i | \(0.226707\pi\) | ||||
−0.756913 | + | 0.653516i | \(0.773293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 291.909 | 0.410561 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −949.898 | + | 949.898i | −1.33226 | + | 1.33226i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −342.606 | − | 342.606i | −0.477833 | − | 0.477833i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 938.565i | 1.30538i | 0.757627 | + | 0.652688i | \(0.226359\pi\) | ||||
−0.757627 | + | 0.652688i | \(0.773641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7163 | 0.0162501 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −486.384 | + | 486.384i | −0.672730 | + | 0.672730i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 404.803 | + | 404.803i | 0.556812 | + | 0.556812i | 0.928398 | − | 0.371586i | \(-0.121186\pi\) |
−0.371586 | + | 0.928398i | \(0.621186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 809.071 | 1.10680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 644.529 | − | 644.529i | 0.879303 | − | 0.879303i | −0.114159 | − | 0.993462i | \(-0.536417\pi\) |
0.993462 | + | 0.114159i | \(0.0364175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 126.030 | + | 126.030i | 0.171004 | + | 0.171004i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1182.11i | 1.59961i | 0.600262 | + | 0.799803i | \(0.295063\pi\) | ||||
−0.600262 | + | 0.799803i | \(0.704937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −297.031 | −0.400851 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −570.681 | + | 570.681i | −0.768077 | + | 0.768077i | −0.977768 | − | 0.209691i | \(-0.932754\pi\) |
0.209691 | + | 0.977768i | \(0.432754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −123.167 | − | 123.167i | −0.164882 | − | 0.164882i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 73.7071i | 0.0984074i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −180.050 | −0.239747 | −0.119873 | − | 0.992789i | \(-0.538249\pi\) | ||||
−0.119873 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −65.9694 | + | 65.9694i | −0.0876087 | + | 0.0876087i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 187.176 | + | 187.176i | 0.247260 | + | 0.247260i | 0.819845 | − | 0.572585i | \(-0.194059\pi\) |
−0.572585 | + | 0.819845i | \(0.694059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 81.0806i | 0.106826i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 912.130 | 1.19859 | 0.599297 | − | 0.800527i | \(-0.295447\pi\) | ||||
0.599297 | + | 0.800527i | \(0.295447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.5551 | − | 53.5551i | 0.0701902 | − | 0.0701902i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −453.069 | − | 453.069i | −0.590703 | − | 0.590703i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 201.778i | 0.262390i | 0.991357 | + | 0.131195i | \(0.0418813\pi\) | ||||
−0.991357 | + | 0.131195i | \(0.958119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −758.686 | −0.984028 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 147.793 | − | 147.793i | 0.191195 | − | 0.191195i | −0.605018 | − | 0.796212i | \(-0.706834\pi\) |
0.796212 | + | 0.605018i | \(0.206834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.8480 | + | 27.8480i | 0.0358404 | + | 0.0358404i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 613.171i | − | 0.787126i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −135.818 | −0.173903 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 161.833 | − | 161.833i | 0.206683 | − | 0.206683i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −447.576 | − | 447.576i | −0.568711 | − | 0.568711i | 0.363056 | − | 0.931767i | \(-0.381733\pi\) |
−0.931767 | + | 0.363056i | \(0.881733\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 315.626i | 0.400032i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.1806 | 0.0419477 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 571.968 | − | 571.968i | 0.721272 | − | 0.721272i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 128.338 | + | 128.338i | 0.161027 | + | 0.161027i | 0.783021 | − | 0.621995i | \(-0.213677\pi\) |
−0.621995 | + | 0.783021i | \(0.713677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 948.345i | − | 1.18691i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −156.606 | −0.195513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −117.823 | + | 117.823i | −0.146728 | + | 0.146728i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −137.449 | − | 137.449i | −0.170322 | − | 0.170322i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 699.212i | − | 0.864292i | −0.901804 | − | 0.432146i | \(-0.857757\pi\) | ||
0.901804 | − | 0.432146i | \(-0.142243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 90.5041 | 0.111596 | 0.0557978 | − | 0.998442i | \(-0.482230\pi\) | ||||
0.0557978 | + | 0.998442i | \(0.482230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −205.287 | + | 205.287i | −0.252506 | + | 0.252506i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −460.808 | − | 460.808i | −0.564025 | − | 0.564025i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 31.5459i | − | 0.0385176i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 250.783 | 0.305461 | 0.152730 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0954 | + | 27.0954i | −0.0329227 | + | 0.0329227i | −0.723377 | − | 0.690454i | \(-0.757411\pi\) |
0.690454 | + | 0.723377i | \(0.257411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 589.930 | + | 589.930i | 0.713337 | + | 0.713337i | 0.967232 | − | 0.253895i | \(-0.0817117\pi\) |
−0.253895 | + | 0.967232i | \(0.581712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1576.77i | 1.90202i | 0.309160 | + | 0.951010i | \(0.399952\pi\) | ||||
−0.309160 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 730.282 | 0.878799 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −539.419 | + | 539.419i | −0.647562 | + | 0.647562i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −163.485 | − | 163.485i | −0.195322 | − | 0.195322i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 963.523i | 1.14842i | 0.818708 | + | 0.574209i | \(0.194690\pi\) | ||||
−0.818708 | + | 0.574209i | \(0.805310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1099.00 | −1.30678 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −412.045 | + | 412.045i | −0.488785 | + | 0.488785i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 65.2883 | + | 65.2883i | 0.0770818 | + | 0.0770818i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 49.3847i | − | 0.0581681i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 881.757 | 1.03614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −254.166 | + | 254.166i | −0.297967 | + | 0.297967i | −0.840217 | − | 0.542250i | \(-0.817573\pi\) |
0.542250 | + | 0.840217i | \(0.317573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 699.206 | + | 699.206i | 0.815876 | + | 0.815876i | 0.985508 | − | 0.169632i | \(-0.0542578\pi\) |
−0.169632 | + | 0.985508i | \(0.554258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 246.708i | 0.287204i | 0.989636 | + | 0.143602i | \(0.0458685\pi\) | ||||
−0.989636 | + | 0.143602i | \(0.954131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 65.1214 | 0.0756346 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1051.01 | + | 1051.01i | −1.21786 | + | 1.21786i | −0.249483 | + | 0.968379i | \(0.580261\pi\) |
−0.968379 | + | 0.249483i | \(0.919739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −49.6197 | − | 49.6197i | −0.0572314 | − | 0.0572314i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 150.869i | 0.173613i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1552.58 | −1.78253 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 111.000 | − | 111.000i | 0.127148 | − | 0.127148i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.2974 | − | 30.2974i | −0.0345467 | − | 0.0345467i | 0.689622 | − | 0.724169i | \(-0.257777\pi\) |
−0.724169 | + | 0.689622i | \(0.757777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 604.009i | − | 0.687155i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 751.294 | 0.852774 | 0.426387 | − | 0.904541i | \(-0.359786\pi\) | ||||
0.426387 | + | 0.904541i | \(0.359786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −666.929 | + | 666.929i | −0.755298 | + | 0.755298i | −0.975463 | − | 0.220164i | \(-0.929341\pi\) |
0.220164 | + | 0.975463i | \(0.429341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −269.662 | − | 269.662i | −0.304015 | − | 0.304015i | 0.538567 | − | 0.842583i | \(-0.318966\pi\) |
−0.842583 | + | 0.538567i | \(0.818966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 72.7286i | − | 0.0818094i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.9546 | −0.0156617 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −540.132 | + | 540.132i | −0.604851 | + | 0.604851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −499.423 | − | 499.423i | −0.556771 | − | 0.556771i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1959.80i | 2.17997i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1214.85 | −1.34833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.9398 | − | 48.9398i | 0.0541969 | − | 0.0541969i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 578.515 | + | 578.515i | 0.637834 | + | 0.637834i | 0.950021 | − | 0.312187i | \(-0.101062\pi\) |
−0.312187 | + | 0.950021i | \(0.601062\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 55.0148i | 0.0605223i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −90.4745 | −0.0993134 | −0.0496567 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496567 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63.6571 | − | 63.6571i | 0.0697231 | − | 0.0697231i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.8138 | + | 47.8138i | 0.0521415 | + | 0.0521415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1467.08i | 1.59639i | 0.602402 | + | 0.798193i | \(0.294210\pi\) | ||||
−0.602402 | + | 0.798193i | \(0.705790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 894.979 | 0.971747 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 836.586 | − | 836.586i | 0.906377 | − | 0.906377i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.9240 | + | 31.9240i | 0.0344379 | + | 0.0344379i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 907.444i | 0.976796i | 0.872621 | + | 0.488398i | \(0.162419\pi\) | ||||
−0.872621 | + | 0.488398i | \(0.837581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 614.454 | 0.659994 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 189.081 | − | 189.081i | 0.202659 | − | 0.202659i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −158.898 | − | 158.898i | −0.169582 | − | 0.169582i | 0.617214 | − | 0.786795i | \(-0.288261\pi\) |
−0.786795 | + | 0.617214i | \(0.788261\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 634.318i | − | 0.675525i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −666.497 | −0.708286 | −0.354143 | − | 0.935191i | \(-0.615227\pi\) | ||||
−0.354143 | + | 0.935191i | \(0.615227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1030.98 | − | 1030.98i | 1.09330 | − | 1.09330i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1038.08 | + | 1038.08i | 1.09618 | + | 1.09618i | 0.994854 | + | 0.101323i | \(0.0323077\pi\) |
0.101323 | + | 0.994854i | \(0.467692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1451.48i | − | 1.52949i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.98979 | 0.00734994 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 262.045 | − | 262.045i | 0.274969 | − | 0.274969i | −0.556128 | − | 0.831097i | \(-0.687714\pi\) |
0.831097 | + | 0.556128i | \(0.187714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 83.6413 | + | 83.6413i | 0.0873995 | + | 0.0873995i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 78.7561i | − | 0.0821232i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1018.80 | 1.06014 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −200.833 | + | 200.833i | −0.208549 | + | 0.208549i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1277.98 | + | 1277.98i | 1.32160 | + | 1.32160i | 0.912484 | + | 0.409111i | \(0.134161\pi\) |
0.409111 | + | 0.912484i | \(0.365839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 346.665i | − | 0.357756i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1640.26 | −1.68924 | −0.844622 | − | 0.535363i | \(-0.820175\pi\) | ||||
−0.844622 | + | 0.535363i | \(0.820175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7786 | + | 12.7786i | −0.0131332 | + | 0.0131332i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 761.480 | + | 761.480i | 0.779406 | + | 0.779406i | 0.979730 | − | 0.200323i | \(-0.0641993\pi\) |
−0.200323 | + | 0.979730i | \(0.564199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 80.9398i | − | 0.0826760i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 291.848 | 0.297500 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 215.035 | − | 215.035i | 0.218754 | − | 0.218754i | −0.589219 | − | 0.807973i | \(-0.700565\pi\) |
0.807973 | + | 0.589219i | \(0.200565\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57.3643 | − | 57.3643i | −0.0581199 | − | 0.0581199i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1549.59i | − | 1.56683i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1240.62 | 1.25189 | 0.625946 | − | 0.779867i | \(-0.284713\pi\) | ||||
0.625946 | + | 0.779867i | \(0.284713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 609.489 | − | 609.489i | 0.613786 | − | 0.613786i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −899.358 | − | 899.358i | −0.902064 | − | 0.902064i | 0.0935507 | − | 0.995615i | \(-0.470178\pi\) |
−0.995615 | + | 0.0935507i | \(0.970178\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 151.757i | 0.151909i |
(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 | 1200.3.bg.e.1057.2 | 4 | ||
4.3 | odd | 2 | 600.3.u.e.457.1 | 4 | |||
5.2 | odd | 4 | 240.3.bg.c.193.1 | 4 | |||
5.3 | odd | 4 | inner | 1200.3.bg.e.193.2 | 4 | ||
5.4 | even | 2 | 240.3.bg.c.97.1 | 4 | |||
12.11 | even | 2 | 1800.3.v.n.1657.1 | 4 | |||
15.2 | even | 4 | 720.3.bh.g.433.1 | 4 | |||
15.14 | odd | 2 | 720.3.bh.g.577.1 | 4 | |||
20.3 | even | 4 | 600.3.u.e.193.1 | 4 | |||
20.7 | even | 4 | 120.3.u.a.73.2 | ✓ | 4 | ||
20.19 | odd | 2 | 120.3.u.a.97.2 | yes | 4 | ||
40.19 | odd | 2 | 960.3.bg.c.577.1 | 4 | |||
40.27 | even | 4 | 960.3.bg.c.193.1 | 4 | |||
40.29 | even | 2 | 960.3.bg.d.577.2 | 4 | |||
40.37 | odd | 4 | 960.3.bg.d.193.2 | 4 | |||
60.23 | odd | 4 | 1800.3.v.n.793.1 | 4 | |||
60.47 | odd | 4 | 360.3.v.b.73.1 | 4 | |||
60.59 | even | 2 | 360.3.v.b.217.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.u.a.73.2 | ✓ | 4 | 20.7 | even | 4 | ||
120.3.u.a.97.2 | yes | 4 | 20.19 | odd | 2 | ||
240.3.bg.c.97.1 | 4 | 5.4 | even | 2 | |||
240.3.bg.c.193.1 | 4 | 5.2 | odd | 4 | |||
360.3.v.b.73.1 | 4 | 60.47 | odd | 4 | |||
360.3.v.b.217.1 | 4 | 60.59 | even | 2 | |||
600.3.u.e.193.1 | 4 | 20.3 | even | 4 | |||
600.3.u.e.457.1 | 4 | 4.3 | odd | 2 | |||
720.3.bh.g.433.1 | 4 | 15.2 | even | 4 | |||
720.3.bh.g.577.1 | 4 | 15.14 | odd | 2 | |||
960.3.bg.c.193.1 | 4 | 40.27 | even | 4 | |||
960.3.bg.c.577.1 | 4 | 40.19 | odd | 2 | |||
960.3.bg.d.193.2 | 4 | 40.37 | odd | 4 | |||
960.3.bg.d.577.2 | 4 | 40.29 | even | 2 | |||
1200.3.bg.e.193.2 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.e.1057.2 | 4 | 1.1 | even | 1 | trivial | ||
1800.3.v.n.793.1 | 4 | 60.23 | odd | 4 | |||
1800.3.v.n.1657.1 | 4 | 12.11 | even | 2 |