Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(193,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, 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("960.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.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: | \(26.1581053786\) |
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 | 577.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.577 |
Dual form | 960.3.bg.d.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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −4.67423 | + | 1.77526i | −0.934847 | + | 0.355051i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.550510 | + | 0.550510i | 0.0786443 | + | 0.0786443i | 0.745335 | − | 0.666690i | \(-0.232290\pi\) |
−0.666690 | + | 0.745335i | \(0.732290\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55051 | −0.140955 | −0.0704777 | − | 0.997513i | \(-0.522452\pi\) | ||||
−0.0704777 | + | 0.997513i | \(0.522452\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −3.55051 | + | 7.89898i | −0.236701 | + | 0.526599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.1464 | + | 11.1464i | 0.655672 | + | 0.655672i | 0.954353 | − | 0.298681i | \(-0.0965466\pi\) |
−0.298681 | + | 0.954353i | \(0.596547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 12.6969i | − | 0.668260i | −0.942527 | − | 0.334130i | \(-0.891558\pi\) | ||
0.942527 | − | 0.334130i | \(-0.108442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.34847 | 0.0642128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.3485 | − | 21.3485i | 0.928194 | − | 0.928194i | −0.0693950 | − | 0.997589i | \(-0.522107\pi\) |
0.997589 | + | 0.0693950i | \(0.0221069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.6969 | − | 16.5959i | 0.747878 | − | 0.663837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 44.0454i | − | 1.51881i | −0.650620 | − | 0.759404i | \(-0.725491\pi\) | ||
0.650620 | − | 0.759404i | \(-0.274509\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −3.55051 | − | 1.59592i | −0.101443 | − | 0.0455977i | ||||
\(36\) | 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 | ||||||||
\(45\) | 5.32577 | + | 14.0227i | 0.118350 | + | 0.311616i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −42.5403 | − | 42.5403i | −0.905113 | − | 0.905113i | 0.0907599 | − | 0.995873i | \(-0.471070\pi\) |
−0.995873 | + | 0.0907599i | \(0.971070\pi\) | |||||||
\(48\) | 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 | ||||||||
\(55\) | 7.24745 | − | 2.75255i | 0.131772 | − | 0.0500464i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.5505 | − | 15.5505i | −0.272816 | − | 0.272816i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 47.4393i | − | 0.804056i | −0.915627 | − | 0.402028i | \(-0.868306\pi\) | ||
0.915627 | − | 0.402028i | \(-0.131694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 59.8888 | 0.981783 | 0.490892 | − | 0.871221i | \(-0.336671\pi\) | ||||
0.490892 | + | 0.871221i | \(0.336671\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.65153 | − | 1.65153i | 0.0262148 | − | 0.0262148i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27.6867 | − | 61.5959i | 0.425950 | − | 0.947630i | ||||
\(66\) | 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 | \(-0.486681\pi\) |
0.999125 | − | 0.0418314i | \(-0.0133192\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.57321 | − | 43.2247i | 0.0343095 | − | 0.576330i | ||||
\(76\) | 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 | ||||||||
\(85\) | −71.8888 | − | 32.3133i | −0.845750 | − | 0.380156i | ||||
\(86\) | 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 | ||||||||
\(95\) | 22.5403 | + | 59.3485i | 0.237266 | + | 0.624721i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37.0000 | − | 37.0000i | −0.381443 | − | 0.381443i | 0.490179 | − | 0.871622i | \(-0.336932\pi\) |
−0.871622 | + | 0.490179i | \(0.836932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.65153i | 0.0469852i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.3383 | 0.181567 | 0.0907835 | − | 0.995871i | \(-0.471063\pi\) | ||||
0.0907835 | + | 0.995871i | \(0.471063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6413 | − | 10.6413i | 0.103314 | − | 0.103314i | −0.653560 | − | 0.756874i | \(-0.726725\pi\) |
0.756874 | + | 0.653560i | \(0.226725\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.30306 | + | 2.39388i | −0.0600292 | + | 0.0227988i | ||||
\(106\) | 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 | \(-0.852759\pi\) | ||
0.894908 | − | 0.446251i | \(-0.147241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −50.5857 | −0.455727 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 30.1362 | − | 30.1362i | 0.266692 | − | 0.266692i | −0.561074 | − | 0.827766i | \(-0.689612\pi\) |
0.827766 | + | 0.561074i | \(0.189612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −61.8888 | + | 137.687i | −0.538163 | + | 1.19728i | ||||
\(116\) | 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 | ||||||||
\(125\) | −57.9319 | + | 110.765i | −0.463455 | + | 0.886120i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −66.0556 | − | 66.0556i | −0.520123 | − | 0.520123i | 0.397486 | − | 0.917608i | \(-0.369883\pi\) |
−0.917608 | + | 0.397486i | \(0.869883\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 88.8990i | 0.689139i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 86.8536 | 0.663004 | 0.331502 | − | 0.943454i | \(-0.392445\pi\) | ||||
0.331502 | + | 0.943454i | \(0.392445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.98979 | − | 6.98979i | 0.0525548 | − | 0.0525548i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23.6969 | + | 10.6515i | 0.175533 | + | 0.0789002i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −71.5301 | − | 71.5301i | −0.522118 | − | 0.522118i | 0.396093 | − | 0.918210i | \(-0.370366\pi\) |
−0.918210 | + | 0.396093i | \(0.870366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.2122i | 0.166995i | 0.996508 | + | 0.0834973i | \(0.0266090\pi\) | ||||
−0.996508 | + | 0.0834973i | \(0.973391\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −104.202 | −0.739022 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.8082 | − | 14.8082i | 0.103554 | − | 0.103554i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 78.1918 | + | 205.879i | 0.539254 | + | 1.41985i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −59.2702 | − | 59.2702i | −0.403198 | − | 0.403198i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 137.530i | − | 0.923021i | −0.887135 | − | 0.461510i | \(-0.847308\pi\) | ||
0.887135 | − | 0.461510i | \(-0.152692\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | −207.980 | + | 78.9898i | −1.34180 | + | 0.509612i | ||||
\(156\) | 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 | ||||||||
\(165\) | 5.50510 | − | 12.2474i | 0.0333643 | − | 0.0742270i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 146.338 | + | 146.338i | 0.876277 | + | 0.876277i | 0.993147 | − | 0.116870i | \(-0.0372861\pi\) |
−0.116870 | + | 0.993147i | \(0.537286\pi\) | |||||||
\(168\) | 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 | ||||||||
\(175\) | 19.4291 | + | 1.15663i | 0.111023 | + | 0.00660933i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −58.1010 | − | 58.1010i | −0.328254 | − | 0.328254i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 77.2372i | 0.431493i | 0.976449 | + | 0.215746i | \(0.0692185\pi\) | ||||
−0.976449 | + | 0.215746i | \(0.930782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −160.656 | −0.887603 | −0.443801 | − | 0.896125i | \(-0.646370\pi\) | ||||
−0.443801 | + | 0.896125i | \(0.646370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73.3485 | − | 73.3485i | 0.400811 | − | 0.400811i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 133.192 | + | 59.8684i | 0.719956 | + | 0.323613i | ||||
\(186\) | 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 | −0.0969302 | − | 0.995291i | \(-0.530902\pi\) |
0.995291 | + | 0.0969302i | \(0.0309024\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −41.5301 | − | 109.348i | −0.212975 | − | 0.560761i | ||||
\(196\) | 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 | ||||||||
\(205\) | 225.732 | − | 85.7321i | 1.10113 | − | 0.418206i | ||||
\(206\) | 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 | \(-0.275908\pi\) | ||||
0.647277 | + | 0.762255i | \(0.275908\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −107.283 | + | 107.283i | −0.503674 | + | 0.503674i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 105.212 | − | 234.070i | 0.489359 | − | 1.08870i | ||||
\(216\) | 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 | −0.980376 | − | 0.197139i | \(-0.936835\pi\) |
0.197139 | + | 0.980376i | \(0.436835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −49.7878 | − | 56.0908i | −0.221279 | − | 0.249293i | ||||
\(226\) | 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 | \(-0.993766\pi\) | ||
0.999808 | − | 0.0195838i | \(-0.00623412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.09082 | −0.00905115 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −50.4699 | + | 50.4699i | −0.216609 | + | 0.216609i | −0.807068 | − | 0.590459i | \(-0.798947\pi\) |
0.590459 | + | 0.807068i | \(0.298947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 274.363 | + | 123.323i | 1.16750 | + | 0.524781i | ||||
\(236\) | 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 | ||||||||
\(245\) | 85.9115 | + | 226.204i | 0.350659 | + | 0.923283i | ||||
\(246\) | 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 | \(-0.465780\pi\) | ||||
0.107298 | + | 0.994227i | \(0.465780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.1010 | + | 33.1010i | −0.130834 | + | 0.130834i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −127.621 | + | 48.4699i | −0.500474 | + | 0.190078i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 309.732 | + | 309.732i | 1.20518 | + | 1.20518i | 0.972569 | + | 0.232614i | \(0.0747280\pi\) |
0.232614 | + | 0.972569i | \(0.425272\pi\) | |||||||
\(258\) | 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 | −0.418349 | − | 0.908286i | \(-0.637391\pi\) |
0.908286 | + | 0.418349i | \(0.137391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −157.980 | + | 351.464i | −0.596149 | + | 1.32628i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −63.9342 | − | 63.9342i | −0.239454 | − | 0.239454i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 112.227i | 0.417201i | 0.978001 | + | 0.208600i | \(0.0668908\pi\) | ||||
−0.978001 | + | 0.208600i | \(0.933109\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −28.9898 | + | 25.7321i | −0.105417 | + | 0.0935714i | ||||
\(276\) | 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 | ||||||||
\(285\) | 100.293 | + | 45.0806i | 0.351905 | + | 0.158178i | ||||
\(286\) | 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 | ||||||||
\(295\) | 84.2168 | + | 221.742i | 0.285481 | + | 0.751669i | ||||
\(296\) | 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 | ||||||||
\(305\) | −279.934 | + | 106.318i | −0.917817 | + | 0.348583i | ||||
\(306\) | 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 | −0.987149 | − | 0.159803i | \(-0.948914\pi\) |
0.159803 | + | 0.987149i | \(0.448914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.78775 | + | 10.6515i | −0.0151992 | + | 0.0338144i | ||||
\(316\) | 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 | ||||||||
\(325\) | −20.0658 | + | 337.065i | −0.0617410 | + | 1.03712i | ||||
\(326\) | 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 | \(-0.770781\pi\) | ||||
−0.751731 | + | 0.659470i | \(0.770781\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −61.9546 | + | 61.9546i | −0.186050 | + | 0.186050i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −524.232 | − | 235.637i | −1.56487 | − | 0.703393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 274.757 | + | 274.757i | 0.815303 | + | 0.815303i | 0.985423 | − | 0.170120i | \(-0.0544156\pi\) |
−0.170120 | + | 0.985423i | \(0.554416\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 92.8332 | + | 244.429i | 0.269082 | + | 0.708490i | ||||
\(346\) | 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 | \(0.0341389\pi\) | ||||
−0.994254 | + | 0.107045i | \(0.965861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 70.1816 | 0.199948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.8332 | + | 34.8332i | −0.0986775 | + | 0.0986775i | −0.754722 | − | 0.656045i | \(-0.772228\pi\) |
0.656045 | + | 0.754722i | \(0.272228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 409.444 | − | 155.505i | 1.15336 | − | 0.438043i | ||||
\(356\) | 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 | ||||||||
\(365\) | −220.293 | + | 490.095i | −0.603542 | + | 1.34273i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 160.056 | + | 160.056i | 0.436119 | + | 0.436119i | 0.890704 | − | 0.454585i | \(-0.150212\pi\) |
−0.454585 | + | 0.890704i | \(0.650212\pi\) | |||||||
\(368\) | 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 | ||||||||
\(375\) | 64.7071 | + | 206.611i | 0.172552 | + | 0.550962i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 420.656 | + | 420.656i | 1.11580 | + | 1.11580i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 424.343i | 1.11964i | 0.828615 | + | 0.559819i | \(0.189129\pi\) | ||||
−0.828615 | + | 0.559819i | \(0.810871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −161.803 | −0.424679 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −325.460 | + | 325.460i | −0.849764 | + | 0.849764i | −0.990103 | − | 0.140339i | \(-0.955181\pi\) |
0.140339 | + | 0.990103i | \(0.455181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.50510 | + | 2.47449i | 0.0142990 | + | 0.00642724i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 108.879 | + | 108.879i | 0.281340 | + | 0.281340i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 698.116i | 1.79464i | 0.441378 | + | 0.897321i | \(0.354490\pi\) | ||||
−0.441378 | + | 0.897321i | \(0.645510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 475.918 | 1.21718 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 106.373 | − | 106.373i | 0.270670 | − | 0.270670i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −172.738 | − | 454.817i | −0.437311 | − | 1.15144i | ||||
\(396\) | 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 | ||||||||
\(405\) | 42.0681 | − | 15.9773i | 0.103872 | − | 0.0394501i | ||||
\(406\) | 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 | ||||||||
\(415\) | −119.019 | + | 264.788i | −0.286794 | + | 0.638043i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.4291 | + | 28.4291i | 0.0681753 | + | 0.0681753i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 414.772i | − | 0.989909i | −0.868919 | − | 0.494955i | \(-0.835185\pi\) | ||
0.868919 | − | 0.494955i | \(-0.164815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −762.727 | −1.81170 | −0.905851 | − | 0.423597i | \(-0.860767\pi\) | ||||
−0.905851 | + | 0.423597i | \(0.860767\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −127.621 | + | 127.621i | −0.301704 | + | 0.301704i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 393.389 | + | 23.4189i | 0.925622 | + | 0.0551032i | ||||
\(426\) | 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 | −0.289919 | − | 0.957051i | \(-0.593628\pi\) |
0.957051 | + | 0.289919i | \(0.0936283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 347.914 | + | 156.384i | 0.799802 | + | 0.359503i | ||||
\(436\) | 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 | ||||||||
\(445\) | 92.6719 | + | 244.005i | 0.208252 | + | 0.548325i | ||||
\(446\) | 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 | ||||||||
\(455\) | 49.1510 | − | 18.6674i | 0.108024 | − | 0.0410272i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.8286 | − | 23.8286i | −0.0521413 | − | 0.0521413i | 0.680555 | − | 0.732697i | \(-0.261739\pi\) |
−0.732697 | + | 0.680555i | \(0.761739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 81.9092i | − | 0.178451i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −44.3179 | −0.0961342 | −0.0480671 | − | 0.998844i | \(-0.515306\pi\) | ||||
−0.0480671 | + | 0.998844i | \(0.515306\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 193.116 | − | 193.116i | 0.417097 | − | 0.417097i | −0.467105 | − | 0.884202i | \(-0.654703\pi\) |
0.884202 | + | 0.467105i | \(0.154703\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −157.980 | + | 351.464i | −0.339741 | + | 0.755837i | ||||
\(466\) | 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 | ||||||||
\(475\) | −210.717 | − | 237.394i | −0.443615 | − | 0.499777i | ||||
\(476\) | 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 | ||||||||
\(485\) | 238.631 | + | 107.262i | 0.492023 | + | 0.221159i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.9444 | + | 41.9444i | 0.0861281 | + | 0.0861281i | 0.748858 | − | 0.662730i | \(-0.230602\pi\) |
−0.662730 | + | 0.748858i | \(0.730602\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 288.000i | − | 0.588957i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −926.468 | −1.88690 | −0.943450 | − | 0.331515i | \(-0.892440\pi\) | ||||
−0.943450 | + | 0.331515i | \(0.892440\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 490.949 | − | 490.949i | 0.995840 | − | 0.995840i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.25765 | − | 21.7423i | −0.0166821 | − | 0.0439239i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −48.2225 | − | 48.2225i | −0.0970271 | − | 0.0970271i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 67.5255i | 0.135322i | 0.997708 | + | 0.0676608i | \(0.0215536\pi\) | ||||
−0.997708 | + | 0.0676608i | \(0.978446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 358.454 | 0.715477 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 180.470 | − | 180.470i | 0.358787 | − | 0.358787i | −0.504579 | − | 0.863366i | \(-0.668352\pi\) |
0.863366 | + | 0.504579i | \(0.168352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −85.7173 | + | 32.5551i | −0.169737 | + | 0.0644655i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.4416 | − | 16.4416i | −0.0324291 | − | 0.0324291i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 920.772i | − | 1.80898i | −0.426493 | − | 0.904491i | \(-0.640251\pi\) | ||
0.426493 | − | 0.904491i | \(-0.359749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 83.6663 | 0.163731 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.6515 | + | 46.6515i | −0.0909387 | + | 0.0909387i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.8490 | + | 68.6311i | −0.0599009 | + | 0.133264i | ||||
\(516\) | 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 | ||||||||
\(525\) | 25.2122 | − | 22.3791i | 0.0480233 | − | 0.0426268i | ||||
\(526\) | 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 | ||||||||
\(535\) | 431.757 | + | 194.070i | 0.807023 | + | 0.362748i | ||||
\(536\) | 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 | \(-0.546207\pi\) | ||||
−0.144654 | + | 0.989482i | \(0.546207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −196.763 | + | 196.763i | −0.362362 | + | 0.362362i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 172.702 | + | 454.722i | 0.316884 | + | 0.834352i | ||||
\(546\) | 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 | ||||||||
\(555\) | 236.449 | − | 89.8025i | 0.426035 | − | 0.161806i | ||||
\(556\) | 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 | ||||||||
\(565\) | −87.3643 | + | 194.363i | −0.154627 | + | 0.344006i | ||||
\(566\) | 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 | \(-0.371972\pi\) | ||||
0.391453 | + | 0.920198i | \(0.371972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −308.474 | + | 308.474i | −0.538350 | + | 0.538350i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.8536 | − | 753.448i | 0.0780062 | − | 1.31035i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −248.444 | − | 248.444i | −0.430579 | − | 0.430579i | 0.458247 | − | 0.888825i | \(-0.348478\pi\) |
−0.888825 | + | 0.458247i | \(0.848478\pi\) | |||||||
\(578\) | 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 | ||||||||
\(585\) | −184.788 | − | 83.0602i | −0.315877 | − | 0.141983i | ||||
\(586\) | 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 | −0.770530 | − | 0.637403i | \(-0.780009\pi\) |
0.637403 | + | 0.770530i | \(0.280009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.7867 | − | 57.3643i | −0.0366163 | − | 0.0964106i | ||||
\(596\) | 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 | ||||||||
\(605\) | 554.345 | − | 210.538i | 0.916273 | − | 0.347997i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −96.8434 | − | 96.8434i | −0.159544 | − | 0.159544i | 0.622821 | − | 0.782365i | \(-0.285987\pi\) |
−0.782365 | + | 0.622821i | \(0.785987\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 171.464 | − | 381.464i | 0.278804 | − | 0.620267i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.9250 | − | 41.9250i | −0.0679498 | − | 0.0679498i | 0.672315 | − | 0.740265i | \(-0.265300\pi\) |
−0.740265 | + | 0.672315i | \(0.765300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 434.363i | − | 0.701718i | −0.936428 | − | 0.350859i | \(-0.885890\pi\) | ||
0.936428 | − | 0.350859i | \(-0.114110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −156.879 | −0.252622 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.7378 | − | 28.7378i | 0.0461280 | − | 0.0461280i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 74.1510 | − | 620.586i | 0.118642 | − | 0.992937i | ||||
\(626\) | 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 | ||||||||
\(635\) | 426.025 | + | 191.494i | 0.670906 | + | 0.301565i | ||||
\(636\) | 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 | ||||||||
\(645\) | −157.818 | − | 415.535i | −0.244680 | − | 0.644240i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 86.3087 | + | 86.3087i | 0.133398 | + | 0.133398i | 0.770653 | − | 0.637255i | \(-0.219930\pi\) |
−0.637255 | + | 0.770653i | \(0.719930\pi\) | |||||||
\(648\) | 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 | ||||||||
\(655\) | −405.974 | + | 154.187i | −0.619808 | + | 0.235400i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −227.969 | − | 227.969i | −0.346985 | − | 0.346985i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1156.80i | 1.75539i | 0.479220 | + | 0.877695i | \(0.340919\pi\) | ||||
−0.479220 | + | 0.877695i | \(0.659081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −908.838 | −1.37494 | −0.687472 | − | 0.726211i | \(-0.741280\pi\) | ||||
−0.687472 | + | 0.726211i | \(0.741280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −260.758 | + | 260.758i | −0.393300 | + | 0.393300i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.2633 | + | 45.0806i | −0.0304711 | + | 0.0677904i | ||||
\(666\) | 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 | \(-0.410196\pi\) |
0.960465 | − | 0.278400i | \(-0.0898040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −129.674 | − | 7.71964i | −0.192110 | − | 0.0114365i | ||||
\(676\) | 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 | ||||||||
\(685\) | 461.333 | + | 207.364i | 0.673478 | + | 0.302722i | ||||
\(686\) | 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 | \(-0.310518\pi\) | ||||
0.560738 | + | 0.827993i | \(0.310518\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.56072 | + | 2.56072i | −0.00369512 | + | 0.00369512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.2077 | − | 108.499i | −0.0592916 | − | 0.156114i | ||||
\(696\) | 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 | \(-0.564073\pi\) | ||||
−0.199935 | + | 0.979809i | \(0.564073\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −262.211 | + | 262.211i | −0.372989 | + | 0.372989i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 487.065 | − | 184.985i | 0.690872 | − | 0.262390i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0954 | + | 10.0954i | 0.0142792 | + | 0.0142792i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 926.686i | − | 1.30703i | −0.756913 | − | 0.653516i | \(-0.773293\pi\) | ||
0.756913 | − | 0.653516i | \(-0.226707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 291.909 | 0.410561 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 949.898 | − | 949.898i | 1.33226 | − | 1.33226i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.9286 | + | 95.5051i | −0.0600399 | + | 0.133574i | ||||
\(716\) | 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 | ||||||||
\(725\) | −730.974 | − | 823.514i | −1.00824 | − | 1.13588i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −404.803 | − | 404.803i | −0.556812 | − | 0.556812i | 0.371586 | − | 0.928398i | \(-0.378814\pi\) |
−0.928398 | + | 0.371586i | \(0.878814\pi\) | |||||||
\(728\) | 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 | ||||||||
\(735\) | 382.262 | + | 171.823i | 0.520085 | + | 0.233773i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −126.030 | − | 126.030i | −0.171004 | − | 0.171004i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1182.11i | − | 1.59961i | −0.600262 | − | 0.799803i | \(-0.704937\pi\) | ||
0.600262 | − | 0.799803i | \(-0.295063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 297.031 | 0.400851 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 570.681 | − | 570.681i | 0.768077 | − | 0.768077i | −0.209691 | − | 0.977768i | \(-0.567246\pi\) |
0.977768 | + | 0.209691i | \(0.0672458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 244.151 | + | 642.848i | 0.327719 | + | 0.862883i | ||||
\(746\) | 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 | ||||||||
\(755\) | −1362.04 | + | 517.298i | −1.80403 | + | 0.685164i | ||||
\(756\) | 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 | ||||||||
\(765\) | −96.9398 | + | 215.666i | −0.126719 | + | 0.281917i | ||||
\(766\) | 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 | ||||||||
\(775\) | 831.918 | − | 738.434i | 1.07344 | − | 0.952818i | ||||
\(776\) | 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 | ||||||||
\(785\) | −339.444 | − | 152.577i | −0.432413 | − | 0.194365i | ||||
\(786\) | 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 | ||||||||
\(795\) | 236.969 | + | 623.939i | 0.298075 | + | 0.784829i | ||||
\(796\) | 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 | ||||||||
\(805\) | −109.868 | + | 41.7276i | −0.136482 | + | 0.0518355i | ||||
\(806\) | 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 | \(-0.517770\pi\) | ||||
−0.0557978 | + | 0.998442i | \(0.517770\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −205.287 | + | 205.287i | −0.252506 | + | 0.252506i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −340.849 | + | 758.302i | −0.418220 | + | 0.930432i | ||||
\(816\) | 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 | \(-0.548807\pi\) | ||||
−0.152730 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.0954 | − | 27.0954i | 0.0329227 | − | 0.0329227i | −0.690454 | − | 0.723377i | \(-0.742589\pi\) |
0.723377 | + | 0.690454i | \(0.242589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.98979 | + | 67.0204i | −0.00483611 | + | 0.0812369i | ||||
\(826\) | 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 | \(-0.600048\pi\) | ||
0.309160 | − | 0.951010i | \(-0.399952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 730.282 | 0.878799 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 539.419 | − | 539.419i | 0.647562 | − | 0.647562i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −943.807 | − | 424.232i | −1.13031 | − | 0.508062i | ||||
\(836\) | 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 | ||||||||
\(845\) | 23.8319 | + | 62.7492i | 0.0282034 | + | 0.0742594i | ||||
\(846\) | 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 | ||||||||
\(855\) | 178.045 | − | 67.6209i | 0.208240 | − | 0.0790888i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −699.206 | − | 699.206i | −0.815876 | − | 0.815876i | 0.169632 | − | 0.985508i | \(-0.445742\pi\) |
−0.985508 | + | 0.169632i | \(0.945742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 246.708i | − | 0.287204i | −0.989636 | − | 0.143602i | \(-0.954131\pi\) | ||
0.989636 | − | 0.143602i | \(-0.0458685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −65.1214 | −0.0756346 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1051.01 | − | 1051.01i | 1.21786 | − | 1.21786i | 0.249483 | − | 0.968379i | \(-0.419739\pi\) |
0.968379 | − | 0.249483i | \(-0.0802605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8786 | − | 24.2020i | 0.0125764 | − | 0.0279792i | ||||
\(866\) | 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 | ||||||||
\(875\) | −92.8694 | + | 29.0852i | −0.106136 | + | 0.0332402i | ||||
\(876\) | 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 | ||||||||
\(885\) | 374.722 | + | 168.434i | 0.423415 | + | 0.190321i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 269.662 | + | 269.662i | 0.304015 | + | 0.304015i | 0.842583 | − | 0.538567i | \(-0.181034\pi\) |
−0.538567 | + | 0.842583i | \(0.681034\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | −137.116 | − | 361.025i | −0.153202 | − | 0.403380i | ||||
\(896\) | 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 | ||||||||
\(905\) | 750.944 | − | 285.206i | 0.829773 | − | 0.315144i | ||||
\(906\) | 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 | ||||||||
\(915\) | −212.636 | + | 473.060i | −0.232389 | + | 0.517006i | ||||
\(916\) | 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 | ||||||||
\(925\) | −728.852 | − | 43.3893i | −0.787948 | − | 0.0469073i | ||||
\(926\) | 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 | ||||||||
\(935\) | 111.464 | + | 50.1021i | 0.119213 | + | 0.0535851i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 158.898 | + | 158.898i | 0.169582 | + | 0.169582i | 0.786795 | − | 0.617214i | \(-0.211739\pi\) |
−0.617214 | + | 0.786795i | \(0.711739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 634.318i | 0.675525i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 666.497 | 0.708286 | 0.354143 | − | 0.935191i | \(-0.384773\pi\) | ||||
0.354143 | + | 0.935191i | \(0.384773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1030.98 | + | 1030.98i | −1.09330 | + | 1.09330i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.18163 | + | 18.9092i | 0.00759961 | + | 0.0200097i | ||||
\(946\) | 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 | −0.831097 | − | 0.556128i | \(-0.812286\pi\) |
0.556128 | + | 0.831097i | \(0.312286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1177.29 | − | 447.131i | 1.23277 | − | 0.468200i | ||||
\(956\) | 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 | ||||||||
\(965\) | −502.636 | + | 1118.24i | −0.520866 | + | 1.15879i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1277.98 | − | 1277.98i | −1.32160 | − | 1.32160i | −0.912484 | − | 0.409111i | \(-0.865839\pi\) |
−0.409111 | − | 0.912484i | \(-0.634161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 346.665i | − | 0.357756i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1640.26 | 1.68924 | 0.844622 | − | 0.535363i | \(-0.179825\pi\) | ||||
0.844622 | + | 0.535363i | \(0.179825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7786 | + | 12.7786i | −0.0131332 | + | 0.0131332i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 388.243 | + | 437.394i | 0.398198 | + | 0.448609i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −761.480 | − | 761.480i | −0.779406 | − | 0.779406i | 0.200323 | − | 0.979730i | \(-0.435801\pi\) |
−0.979730 | + | 0.200323i | \(0.935801\pi\) | |||||||
\(978\) | 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 | −0.807973 | − | 0.589219i | \(-0.799435\pi\) |
0.589219 | + | 0.807973i | \(0.299435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.4847 | − | 6.06123i | −0.0136900 | − | 0.00615353i | ||||
\(986\) | 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 | ||||||||
\(995\) | −540.681 | − | 1423.61i | −0.543398 | − | 1.43076i | ||||
\(996\) | 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 | 960.3.bg.d.577.2 | 4 | ||
4.3 | odd | 2 | 960.3.bg.c.577.1 | 4 | |||
5.3 | odd | 4 | inner | 960.3.bg.d.193.2 | 4 | ||
8.3 | odd | 2 | 120.3.u.a.97.2 | yes | 4 | ||
8.5 | even | 2 | 240.3.bg.c.97.1 | 4 | |||
20.3 | even | 4 | 960.3.bg.c.193.1 | 4 | |||
24.5 | odd | 2 | 720.3.bh.g.577.1 | 4 | |||
24.11 | even | 2 | 360.3.v.b.217.1 | 4 | |||
40.3 | even | 4 | 120.3.u.a.73.2 | ✓ | 4 | ||
40.13 | odd | 4 | 240.3.bg.c.193.1 | 4 | |||
40.19 | odd | 2 | 600.3.u.e.457.1 | 4 | |||
40.27 | even | 4 | 600.3.u.e.193.1 | 4 | |||
40.29 | even | 2 | 1200.3.bg.e.1057.2 | 4 | |||
40.37 | odd | 4 | 1200.3.bg.e.193.2 | 4 | |||
120.53 | even | 4 | 720.3.bh.g.433.1 | 4 | |||
120.59 | even | 2 | 1800.3.v.n.1657.1 | 4 | |||
120.83 | odd | 4 | 360.3.v.b.73.1 | 4 | |||
120.107 | odd | 4 | 1800.3.v.n.793.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.u.a.73.2 | ✓ | 4 | 40.3 | even | 4 | ||
120.3.u.a.97.2 | yes | 4 | 8.3 | odd | 2 | ||
240.3.bg.c.97.1 | 4 | 8.5 | even | 2 | |||
240.3.bg.c.193.1 | 4 | 40.13 | odd | 4 | |||
360.3.v.b.73.1 | 4 | 120.83 | odd | 4 | |||
360.3.v.b.217.1 | 4 | 24.11 | even | 2 | |||
600.3.u.e.193.1 | 4 | 40.27 | even | 4 | |||
600.3.u.e.457.1 | 4 | 40.19 | odd | 2 | |||
720.3.bh.g.433.1 | 4 | 120.53 | even | 4 | |||
720.3.bh.g.577.1 | 4 | 24.5 | odd | 2 | |||
960.3.bg.c.193.1 | 4 | 20.3 | even | 4 | |||
960.3.bg.c.577.1 | 4 | 4.3 | odd | 2 | |||
960.3.bg.d.193.2 | 4 | 5.3 | odd | 4 | inner | ||
960.3.bg.d.577.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.e.193.2 | 4 | 40.37 | odd | 4 | |||
1200.3.bg.e.1057.2 | 4 | 40.29 | even | 2 | |||
1800.3.v.n.793.1 | 4 | 120.107 | odd | 4 | |||
1800.3.v.n.1657.1 | 4 | 120.59 | even | 2 |