Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(73,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.73");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.j (of order \(4\), degree \(2\), 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: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1579585536.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(2.22833 + 1.32913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.73 |
Dual form | 156.3.j.a.109.2 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.92621 | + | 1.92621i | 0.385242 | + | 0.385242i | 0.872986 | − | 0.487744i | \(-0.162180\pi\) |
−0.487744 | + | 0.872986i | \(0.662180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.58447 | + | 3.58447i | −0.512067 | + | 0.512067i | −0.915159 | − | 0.403092i | \(-0.867935\pi\) |
0.403092 | + | 0.915159i | \(0.367935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.83954 | + | 6.83954i | −0.621776 | + | 0.621776i | −0.945985 | − | 0.324209i | \(-0.894902\pi\) |
0.324209 | + | 0.945985i | \(0.394902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.86475 | + | 12.0555i | 0.374212 | + | 0.927343i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.33629 | − | 3.33629i | −0.222420 | − | 0.222420i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.4992i | 1.32348i | 0.749731 | + | 0.661742i | \(0.230183\pi\) | ||||
−0.749731 | + | 0.661742i | \(0.769817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26106 | + | 1.26106i | 0.0663716 | + | 0.0663716i | 0.739513 | − | 0.673142i | \(-0.235056\pi\) |
−0.673142 | + | 0.739513i | \(0.735056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.20849 | − | 6.20849i | 0.295642 | − | 0.295642i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.8702i | 1.55957i | 0.626045 | + | 0.779787i | \(0.284672\pi\) | ||||
−0.626045 | + | 0.779787i | \(0.715328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 17.5794i | − | 0.703177i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29185 | 0.182478 | 0.0912389 | − | 0.995829i | \(-0.470917\pi\) | ||||
0.0912389 | + | 0.995829i | \(0.470917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.8901 | − | 22.8901i | −0.738390 | − | 0.738390i | 0.233876 | − | 0.972266i | \(-0.424859\pi\) |
−0.972266 | + | 0.233876i | \(0.924859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.8464 | − | 11.8464i | 0.358983 | − | 0.358983i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.8089 | −0.394540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.7791 | − | 27.7791i | 0.750787 | − | 0.750787i | −0.223839 | − | 0.974626i | \(-0.571859\pi\) |
0.974626 | + | 0.223839i | \(0.0718590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.42600 | − | 20.8807i | −0.216051 | − | 0.535402i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.72861 | − | 2.72861i | −0.0665516 | − | 0.0665516i | 0.673048 | − | 0.739599i | \(-0.264985\pi\) |
−0.739599 | + | 0.673048i | \(0.764985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 53.4988i | − | 1.24416i | −0.782954 | − | 0.622079i | \(-0.786288\pi\) | ||
0.782954 | − | 0.622079i | \(-0.213712\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.77863 | + | 5.77863i | 0.128414 | + | 0.128414i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.5386 | − | 24.5386i | 0.522097 | − | 0.522097i | −0.396107 | − | 0.918204i | \(-0.629639\pi\) |
0.918204 | + | 0.396107i | \(0.129639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.3031i | 0.475574i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 38.9698i | − | 0.764114i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.8175 | 0.392784 | 0.196392 | − | 0.980525i | \(-0.437078\pi\) | ||||
0.196392 | + | 0.980525i | \(0.437078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −26.3488 | −0.479069 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18422 | − | 2.18422i | −0.0383197 | − | 0.0383197i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −38.5988 | + | 38.5988i | −0.654217 | + | 0.654217i | −0.954006 | − | 0.299789i | \(-0.903084\pi\) |
0.299789 | + | 0.954006i | \(0.403084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.7505 | 0.323778 | 0.161889 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161889 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.7534 | + | 10.7534i | −0.170689 | + | 0.170689i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.8508 | + | 32.5919i | −0.213089 | + | 0.501414i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.69940 | − | 6.69940i | −0.0999910 | − | 0.0999910i | 0.655342 | − | 0.755333i | \(-0.272525\pi\) |
−0.755333 | + | 0.655342i | \(0.772525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 62.1290i | − | 0.900420i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35.7577 | + | 35.7577i | 0.503629 | + | 0.503629i | 0.912564 | − | 0.408935i | \(-0.134100\pi\) |
−0.408935 | + | 0.912564i | \(0.634100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.0975 | − | 68.0975i | 0.932843 | − | 0.932843i | −0.0650398 | − | 0.997883i | \(-0.520717\pi\) |
0.997883 | + | 0.0650398i | \(0.0207174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30.4485i | 0.405980i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 49.0323i | − | 0.636783i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.68606 | 0.0466590 | 0.0233295 | − | 0.999728i | \(-0.492573\pi\) | ||||
0.0233295 | + | 0.999728i | \(0.492573\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −40.8170 | − | 40.8170i | −0.491772 | − | 0.491772i | 0.417093 | − | 0.908864i | \(-0.363049\pi\) |
−0.908864 | + | 0.417093i | \(0.863049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −43.3383 | + | 43.3383i | −0.509862 | + | 0.509862i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.16576 | −0.105354 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −70.1454 | + | 70.1454i | −0.788151 | + | 0.788151i | −0.981191 | − | 0.193040i | \(-0.938165\pi\) |
0.193040 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.6500 | − | 25.7749i | −0.666484 | − | 0.283240i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 39.6468 | + | 39.6468i | 0.426310 | + | 0.426310i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.85813i | 0.0511383i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 115.441 | + | 115.441i | 1.19011 | + | 1.19011i | 0.977035 | + | 0.213080i | \(0.0683494\pi\) |
0.213080 | + | 0.977035i | \(0.431651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.5186 | + | 20.5186i | −0.207259 | + | 0.207259i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36.6504i | 0.362875i | 0.983402 | + | 0.181438i | \(0.0580750\pi\) | ||||
−0.983402 | + | 0.181438i | \(0.941925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 130.389i | 1.26592i | 0.774186 | + | 0.632958i | \(0.218159\pi\) | ||||
−0.774186 | + | 0.632958i | \(0.781841\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23.9177 | 0.227788 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 162.941 | 1.52281 | 0.761407 | − | 0.648274i | \(-0.224509\pi\) | ||||
0.761407 | + | 0.648274i | \(0.224509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −98.1123 | − | 98.1123i | −0.900113 | − | 0.900113i | 0.0953329 | − | 0.995445i | \(-0.469608\pi\) |
−0.995445 | + | 0.0953329i | \(0.969608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −48.1149 | + | 48.1149i | −0.433467 | + | 0.433467i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −26.8171 | −0.237320 | −0.118660 | − | 0.992935i | \(-0.537860\pi\) | ||||
−0.118660 | + | 0.992935i | \(0.537860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −69.0935 | + | 69.0935i | −0.600813 | + | 0.600813i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5943 | + | 36.1664i | 0.124737 | + | 0.309114i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −80.6479 | − | 80.6479i | −0.677713 | − | 0.677713i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.4414i | 0.226789i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.72610 | + | 4.72610i | 0.0384236 | + | 0.0384236i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 82.0169 | − | 82.0169i | 0.656135 | − | 0.656135i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 124.496i | 0.980282i | 0.871643 | + | 0.490141i | \(0.163055\pi\) | ||||
−0.871643 | + | 0.490141i | \(0.836945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 92.6627i | 0.718315i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 246.156 | 1.87906 | 0.939529 | − | 0.342471i | \(-0.111264\pi\) | ||||
0.939529 | + | 0.342471i | \(0.111264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.04047 | −0.0679734 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0089 | − | 10.0089i | −0.0741399 | − | 0.0741399i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −106.209 | + | 106.209i | −0.775248 | + | 0.775248i | −0.979019 | − | 0.203771i | \(-0.934680\pi\) |
0.203771 | + | 0.979019i | \(0.434680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −54.0949 | −0.389172 | −0.194586 | − | 0.980885i | \(-0.562336\pi\) | ||||
−0.194586 | + | 0.980885i | \(0.562336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −42.5021 | + | 42.5021i | −0.301433 | + | 0.301433i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −115.726 | − | 49.1811i | −0.809276 | − | 0.343924i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1932 | + | 10.1932i | 0.0702981 | + | 0.0702981i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 40.3622i | − | 0.274573i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −159.415 | − | 159.415i | −1.06990 | − | 1.06990i | −0.997366 | − | 0.0725343i | \(-0.976891\pi\) |
−0.0725343 | − | 0.997366i | \(-0.523109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.8748 | − | 18.8748i | 0.124999 | − | 0.124999i | −0.641840 | − | 0.766839i | \(-0.721829\pi\) |
0.766839 | + | 0.641840i | \(0.221829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 67.4977i | 0.441162i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 88.1823i | − | 0.568918i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 265.777 | 1.69285 | 0.846423 | − | 0.532510i | \(-0.178751\pi\) | ||||
0.846423 | + | 0.532510i | \(0.178751\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −36.0570 | −0.226774 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −128.576 | − | 128.576i | −0.798607 | − | 0.798607i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 114.497 | − | 114.497i | 0.702437 | − | 0.702437i | −0.262496 | − | 0.964933i | \(-0.584546\pi\) |
0.964933 | + | 0.262496i | \(0.0845456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 45.6374 | 0.276590 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 152.956 | − | 152.956i | 0.915905 | − | 0.915905i | −0.0808233 | − | 0.996728i | \(-0.525755\pi\) |
0.996728 | + | 0.0808233i | \(0.0257550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −121.668 | + | 117.294i | −0.719931 | + | 0.694046i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.78318 | + | 3.78318i | 0.0221239 | + | 0.0221239i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 243.771i | − | 1.40908i | −0.709664 | − | 0.704540i | \(-0.751153\pi\) | ||
0.709664 | − | 0.704540i | \(-0.248847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 63.0130 | + | 63.0130i | 0.360074 | + | 0.360074i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 66.8551 | − | 66.8551i | 0.377712 | − | 0.377712i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 86.8648i | 0.485278i | 0.970117 | + | 0.242639i | \(0.0780131\pi\) | ||||
−0.970117 | + | 0.242639i | \(0.921987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 168.352i | − | 0.930121i | −0.885279 | − | 0.465061i | \(-0.846032\pi\) | ||
0.885279 | − | 0.465061i | \(-0.153968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −34.2088 | −0.186933 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 107.017 | 0.578470 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −153.884 | − | 153.884i | −0.822911 | − | 0.822911i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.6255 | − | 18.6255i | 0.0985474 | − | 0.0985474i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 325.900 | 1.70628 | 0.853141 | − | 0.521680i | \(-0.174695\pi\) | ||||
0.853141 | + | 0.521680i | \(0.174695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −231.123 | + | 231.123i | −1.19753 | + | 1.19753i | −0.222625 | + | 0.974904i | \(0.571462\pi\) |
−0.974904 | + | 0.222625i | \(0.928538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.9903 | − | 56.4508i | 0.123027 | − | 0.289491i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −248.700 | − | 248.700i | −1.26244 | − | 1.26244i | −0.949909 | − | 0.312527i | \(-0.898825\pi\) |
−0.312527 | − | 0.949909i | \(-0.601175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 244.539i | − | 1.22884i | −0.788980 | − | 0.614419i | \(-0.789391\pi\) | ||
0.788980 | − | 0.614419i | \(-0.210609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6037 | + | 11.6037i | 0.0577298 | + | 0.0577298i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.9685 | + | 18.9685i | −0.0934409 | + | 0.0934409i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 10.5118i | − | 0.0512769i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 107.611i | 0.519858i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.2501 | −0.0825365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6759 | −0.112208 | −0.0561041 | − | 0.998425i | \(-0.517868\pi\) | ||||
−0.0561041 | + | 0.998425i | \(0.517868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −61.9341 | − | 61.9341i | −0.290770 | − | 0.290770i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 103.050 | − | 103.050i | 0.479302 | − | 0.479302i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 164.098 | 0.756211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −117.948 | + | 117.948i | −0.538577 | + | 0.538577i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −271.239 | + | 109.453i | −1.22732 | + | 0.495264i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 136.609 | + | 136.609i | 0.612595 | + | 0.612595i | 0.943622 | − | 0.331026i | \(-0.107395\pi\) |
−0.331026 | + | 0.943622i | \(0.607395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 52.7383i | − | 0.234392i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 218.098 | + | 218.098i | 0.960782 | + | 0.960782i | 0.999259 | − | 0.0384775i | \(-0.0122508\pi\) |
−0.0384775 | + | 0.999259i | \(0.512251\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 35.0435 | − | 35.0435i | 0.153028 | − | 0.153028i | −0.626441 | − | 0.779469i | \(-0.715489\pi\) |
0.779469 | + | 0.626441i | \(0.215489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 84.9264i | 0.367647i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 44.4323i | 0.190697i | 0.995444 | + | 0.0953483i | \(0.0303965\pi\) | ||||
−0.995444 | + | 0.0953483i | \(0.969604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 94.5329 | 0.402268 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.38444 | −0.0269386 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −133.935 | − | 133.935i | −0.560396 | − | 0.560396i | 0.369024 | − | 0.929420i | \(-0.379692\pi\) |
−0.929420 | + | 0.369024i | \(0.879692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −115.524 | + | 115.524i | −0.479351 | + | 0.479351i | −0.904924 | − | 0.425573i | \(-0.860073\pi\) |
0.425573 | + | 0.904924i | \(0.360073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.8867 | + | 44.8867i | −0.183211 | + | 0.183211i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.06791 | + | 21.3374i | −0.0367122 | + | 0.0863863i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 70.6972 | + | 70.6972i | 0.283924 | + | 0.283924i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 380.503i | 1.51595i | 0.652284 | + | 0.757975i | \(0.273811\pi\) | ||||
−0.652284 | + | 0.757975i | \(0.726189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.335 | − | 245.335i | −0.969705 | − | 0.969705i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 75.0641 | − | 75.0641i | 0.294369 | − | 0.294369i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 293.869i | 1.14346i | 0.820442 | + | 0.571730i | \(0.193727\pi\) | ||||
−0.820442 | + | 0.571730i | \(0.806273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 199.147i | 0.768907i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.8756 | 0.0608259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 157.450 | 0.598671 | 0.299335 | − | 0.954148i | \(-0.403235\pi\) | ||||
0.299335 | + | 0.954148i | \(0.403235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.0990 | + | 40.0990i | 0.151317 | + | 0.151317i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 121.495 | − | 121.495i | 0.455039 | − | 0.455039i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 174.739 | 0.649586 | 0.324793 | − | 0.945785i | \(-0.394705\pi\) | ||||
0.324793 | + | 0.945785i | \(0.394705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8688 | − | 15.8688i | 0.0585564 | − | 0.0585564i | −0.677222 | − | 0.735779i | \(-0.736816\pi\) |
0.735779 | + | 0.677222i | \(0.236816\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 105.049 | + | 44.6434i | 0.384795 | + | 0.163529i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 120.235 | + | 120.235i | 0.437219 | + | 0.437219i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 241.083i | − | 0.870335i | −0.900350 | − | 0.435167i | \(-0.856689\pi\) | ||
0.900350 | − | 0.435167i | \(-0.143311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −68.6703 | − | 68.6703i | −0.246130 | − | 0.246130i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −149.037 | + | 149.037i | −0.530381 | + | 0.530381i | −0.920686 | − | 0.390305i | \(-0.872370\pi\) |
0.390305 | + | 0.920686i | \(0.372370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 350.794i | 1.23956i | 0.784777 | + | 0.619778i | \(0.212777\pi\) | ||||
−0.784777 | + | 0.619778i | \(0.787223\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 8.41453i | − | 0.0295247i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.5613 | 0.0681578 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −217.216 | −0.751612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −199.950 | − | 199.950i | −0.687113 | − | 0.687113i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −349.661 | + | 349.661i | −1.19338 | + | 1.19338i | −0.217270 | + | 0.976112i | \(0.569715\pi\) |
−0.976112 | + | 0.217270i | \(0.930285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −148.699 | −0.504064 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.5393 | − | 35.5393i | 0.119661 | − | 0.119661i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −432.432 | + | 174.500i | −1.44626 | + | 0.583611i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 191.765 | + | 191.765i | 0.637093 | + | 0.637093i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 63.4803i | − | 0.209506i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 38.0435 | + | 38.0435i | 0.124733 | + | 0.124733i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 397.145 | − | 397.145i | 1.29363 | − | 1.29363i | 0.361109 | − | 0.932524i | \(-0.382398\pi\) |
0.932524 | − | 0.361109i | \(-0.117602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 225.841i | − | 0.730877i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 157.872i | − | 0.507626i | −0.967253 | − | 0.253813i | \(-0.918315\pi\) | ||
0.967253 | − | 0.253813i | \(-0.0816847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 87.3756 | 0.279155 | 0.139578 | − | 0.990211i | \(-0.455426\pi\) | ||||
0.139578 | + | 0.990211i | \(0.455426\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −41.4267 | −0.131513 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 351.590 | + | 351.590i | 1.10912 | + | 1.10912i | 0.993267 | + | 0.115850i | \(0.0369591\pi\) |
0.115850 | + | 0.993267i | \(0.463041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.1938 | + | 36.1938i | −0.113460 | + | 0.113460i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −282.222 | −0.879197 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.3729 | + | 28.3729i | −0.0878418 | + | 0.0878418i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 211.928 | − | 85.5196i | 0.652087 | − | 0.263137i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 169.935 | + | 169.935i | 0.519680 | + | 0.519680i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 175.916i | 0.534698i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −67.6157 | − | 67.6157i | −0.204277 | − | 0.204277i | 0.597553 | − | 0.801830i | \(-0.296140\pi\) |
−0.801830 | + | 0.597553i | \(0.796140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83.3374 | − | 83.3374i | 0.250262 | − | 0.250262i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 25.8089i | − | 0.0770415i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 205.231i | 0.608995i | 0.952513 | + | 0.304497i | \(0.0984885\pi\) | ||||
−0.952513 | + | 0.304497i | \(0.901512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 46.4486 | 0.137017 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 313.115 | 0.918227 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −259.168 | − | 259.168i | −0.755593 | − | 0.755593i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 119.673 | − | 119.673i | 0.346880 | − | 0.346880i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −216.750 | −0.624639 | −0.312319 | − | 0.949977i | \(-0.601106\pi\) | ||||
−0.312319 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −82.0098 | + | 82.0098i | −0.234985 | + | 0.234985i | −0.814770 | − | 0.579785i | \(-0.803137\pi\) |
0.579785 | + | 0.814770i | \(0.303137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.2780 | − | 62.6420i | −0.0720171 | − | 0.178467i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −193.665 | − | 193.665i | −0.548627 | − | 0.548627i | 0.377417 | − | 0.926044i | \(-0.376812\pi\) |
−0.926044 | + | 0.377417i | \(0.876812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 137.754i | 0.388038i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 139.686 | + | 139.686i | 0.391278 | + | 0.391278i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −170.887 | + | 170.887i | −0.476010 | + | 0.476010i | −0.903853 | − | 0.427843i | \(-0.859274\pi\) |
0.427843 | + | 0.903853i | \(0.359274\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 357.819i | − | 0.991190i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 47.5300i | − | 0.130937i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 262.340 | 0.718741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 517.394 | 1.40979 | 0.704896 | − | 0.709310i | \(-0.250994\pi\) | ||||
0.704896 | + | 0.709310i | \(0.250994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.18584 | − | 8.18584i | −0.0221839 | − | 0.0221839i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −74.6199 | + | 74.6199i | −0.201132 | + | 0.201132i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.9133 | −0.0694727 | −0.0347364 | − | 0.999397i | \(-0.511059\pi\) | ||||
−0.0347364 | + | 0.999397i | \(0.511059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −142.057 | + | 142.057i | −0.378820 | + | 0.378820i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.7436 | + | 63.7957i | 0.0682853 | + | 0.169219i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −351.980 | − | 351.980i | −0.928708 | − | 0.928708i | 0.0689146 | − | 0.997623i | \(-0.478046\pi\) |
−0.997623 | + | 0.0689146i | \(0.978046\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 215.633i | − | 0.565966i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.97886 | − | 3.97886i | −0.0103887 | − | 0.0103887i | 0.701893 | − | 0.712282i | \(-0.252338\pi\) |
−0.712282 | + | 0.701893i | \(0.752338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 94.4464 | − | 94.4464i | 0.245315 | − | 0.245315i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 160.496i | − | 0.414720i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 420.725i | − | 1.08156i | −0.841165 | − | 0.540778i | \(-0.818130\pi\) | ||
0.841165 | − | 0.540778i | \(-0.181870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −807.052 | −2.06407 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −426.356 | −1.08487 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.10013 | + | 7.10013i | 0.0179750 | + | 0.0179750i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 251.922 | − | 251.922i | 0.634563 | − | 0.634563i | −0.314646 | − | 0.949209i | \(-0.601886\pi\) |
0.949209 | + | 0.314646i | \(0.101886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.6585 | 0.0392445 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 544.359 | − | 544.359i | 1.35750 | − | 1.35750i | 0.480521 | − | 0.876983i | \(-0.340448\pi\) |
0.876983 | − | 0.480521i | \(-0.159552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 164.596 | − | 387.306i | 0.408427 | − | 0.961056i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.3359 | + | 17.3359i | 0.0428047 | + | 0.0428047i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 379.993i | 0.933643i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 210.815 | + | 210.815i | 0.515439 | + | 0.515439i | 0.916188 | − | 0.400749i | \(-0.131250\pi\) |
−0.400749 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 183.959 | − | 183.959i | 0.447589 | − | 0.447589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 276.713i | − | 0.670006i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 157.244i | − | 0.378902i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 93.6951 | 0.224688 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 75.7366 | 0.180756 | 0.0903778 | − | 0.995908i | \(-0.471193\pi\) | ||||
0.0903778 | + | 0.995908i | \(0.471193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.9020 | + | 37.9020i | 0.0900286 | + | 0.0900286i | 0.750687 | − | 0.660658i | \(-0.229723\pi\) |
−0.660658 | + | 0.750687i | \(0.729723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 73.6157 | − | 73.6157i | 0.174032 | − | 0.174032i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 395.524 | 0.930644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −70.7949 | + | 70.7949i | −0.165796 | + | 0.165796i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 200.444 | + | 85.1842i | 0.467236 | + | 0.198565i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −534.376 | − | 534.376i | −1.23985 | − | 1.23985i | −0.960061 | − | 0.279789i | \(-0.909735\pi\) |
−0.279789 | − | 0.960061i | \(-0.590265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 700.849i | − | 1.61859i | −0.587402 | − | 0.809295i | \(-0.699849\pi\) | ||
0.587402 | − | 0.809295i | \(-0.300151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.6552 | − | 17.6552i | −0.0405866 | − | 0.0405866i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.2345 | + | 45.2345i | −0.103511 | + | 0.103511i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 97.5970i | 0.222317i | 0.993803 | + | 0.111158i | \(0.0354561\pi\) | ||||
−0.993803 | + | 0.111158i | \(0.964544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 69.9094i | 0.158525i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −264.575 | −0.597234 | −0.298617 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298617 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −270.230 | −0.607258 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 276.115 | + | 276.115i | 0.617707 | + | 0.617707i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −416.268 | + | 416.268i | −0.927101 | + | 0.927101i | −0.997518 | − | 0.0704170i | \(-0.977567\pi\) |
0.0704170 | + | 0.997518i | \(0.477567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.3249 | 0.0827603 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.6921 | + | 32.6921i | −0.0721680 | + | 0.0721680i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −67.1769 | − | 166.473i | −0.147641 | − | 0.365874i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 431.567 | + | 431.567i | 0.944347 | + | 0.944347i | 0.998531 | − | 0.0541838i | \(-0.0172557\pi\) |
−0.0541838 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 116.909i | − | 0.254705i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4845 | + | 18.4845i | 0.0400965 | + | 0.0400965i | 0.726871 | − | 0.686774i | \(-0.240974\pi\) |
−0.686774 | + | 0.726871i | \(0.740974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −547.447 | + | 547.447i | −1.18239 | + | 1.18239i | −0.203267 | + | 0.979123i | \(0.565156\pi\) |
−0.979123 | + | 0.203267i | \(0.934844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 152.736i | 0.328465i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 155.958i | − | 0.333957i | −0.985961 | − | 0.166979i | \(-0.946599\pi\) | ||
0.985961 | − | 0.166979i | \(-0.0534011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0276 | 0.102404 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −460.339 | −0.977366 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 365.907 | + | 365.907i | 0.773588 | + | 0.773588i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.1687 | − | 22.1687i | 0.0466710 | − | 0.0466710i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 62.4526 | 0.130928 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 406.516 | − | 406.516i | 0.848677 | − | 0.848677i | −0.141291 | − | 0.989968i | \(-0.545125\pi\) |
0.989968 | + | 0.141291i | \(0.0451253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 470.029 | + | 199.752i | 0.977191 | + | 0.415284i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 222.700 | + | 222.700i | 0.461076 | + | 0.461076i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 444.728i | 0.916964i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 183.739 | + | 183.739i | 0.377288 | + | 0.377288i | 0.870123 | − | 0.492835i | \(-0.164039\pi\) |
−0.492835 | + | 0.870123i | \(0.664039\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −198.315 | + | 198.315i | −0.405552 | + | 0.405552i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 100.574i | − | 0.204836i | −0.994741 | − | 0.102418i | \(-0.967342\pi\) | ||
0.994741 | − | 0.102418i | \(-0.0326579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 119.063i | 0.241507i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −79.0463 | −0.159690 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −256.345 | −0.515784 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 344.530 | + | 344.530i | 0.690441 | + | 0.690441i | 0.962329 | − | 0.271888i | \(-0.0876480\pi\) |
−0.271888 | + | 0.962329i | \(0.587648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −264.928 | + | 264.928i | −0.528798 | + | 0.528798i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −592.672 | −1.17827 | −0.589137 | − | 0.808033i | \(-0.700532\pi\) | ||||
−0.589137 | + | 0.808033i | \(0.700532\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −70.5963 | + | 70.5963i | −0.139795 | + | 0.139795i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 210.736 | − | 203.159i | 0.415652 | − | 0.400707i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −338.778 | − | 338.778i | −0.665575 | − | 0.665575i | 0.291113 | − | 0.956689i | \(-0.405974\pi\) |
−0.956689 | + | 0.291113i | \(0.905974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 488.187i | 0.955357i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.55266 | − | 6.55266i | −0.0127732 | − | 0.0127732i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −251.157 | + | 251.157i | −0.487684 | + | 0.487684i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 335.665i | 0.649255i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 422.224i | 0.813533i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 816.440 | 1.56706 | 0.783531 | − | 0.621352i | \(-0.213416\pi\) | ||||
0.783531 | + | 0.621352i | \(0.213416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −146.348 | −0.279825 | −0.139912 | − | 0.990164i | \(-0.544682\pi\) | ||||
−0.139912 | + | 0.990164i | \(0.544682\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −109.142 | − | 109.142i | −0.207889 | − | 0.207889i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 515.010 | − | 515.010i | 0.977249 | − | 0.977249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −757.670 | −1.43227 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −115.796 | + | 115.796i | −0.218072 | + | 0.218072i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.6207 | − | 46.1687i | 0.0368118 | − | 0.0866205i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 313.859 | + | 313.859i | 0.586652 | + | 0.586652i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 150.454i | − | 0.280176i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −159.383 | − | 159.383i | −0.295701 | − | 0.295701i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −587.359 | + | 587.359i | −1.08569 | + | 1.08569i | −0.0897247 | + | 0.995967i | \(0.528599\pi\) |
−0.995967 | + | 0.0897247i | \(0.971401\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 291.594i | 0.537006i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 377.970i | − | 0.693522i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −304.970 | −0.557531 | −0.278766 | − | 0.960359i | \(-0.589925\pi\) | ||||
−0.278766 | + | 0.960359i | \(0.589925\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 59.2514 | 0.107926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.67335 | + | 6.67335i | 0.0121113 | + | 0.0121113i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.2126 | + | 13.2126i | −0.0238925 | + | 0.0238925i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −185.359 | −0.333980 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 414.483 | − | 414.483i | 0.744135 | − | 0.744135i | −0.229236 | − | 0.973371i | \(-0.573623\pi\) |
0.973371 | + | 0.229236i | \(0.0736228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 644.953 | − | 260.259i | 1.15376 | − | 0.465579i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 266.536 | + | 266.536i | 0.475108 | + | 0.475108i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1016.06i | 1.80472i | 0.430985 | + | 0.902359i | \(0.358166\pi\) | ||||
−0.430985 | + | 0.902359i | \(0.641834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −51.6554 | − | 51.6554i | −0.0914256 | − | 0.0914256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −32.2602 | + | 32.2602i | −0.0568964 | + | 0.0568964i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 563.561i | − | 0.990442i | −0.868767 | − | 0.495221i | \(-0.835087\pi\) | ||
0.868767 | − | 0.495221i | \(-0.164913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 402.182i | 0.704347i | 0.935935 | + | 0.352174i | \(0.114557\pi\) | ||||
−0.935935 | + | 0.352174i | \(0.885443\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −564.475 | −0.985122 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 630.577 | 1.09666 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 338.309 | + | 338.309i | 0.586325 | + | 0.586325i | 0.936634 | − | 0.350309i | \(-0.113924\pi\) |
−0.350309 | + | 0.936634i | \(0.613924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 400.317 | − | 400.317i | 0.691394 | − | 0.691394i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 292.615 | 0.503640 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −142.382 | + | 142.382i | −0.244224 | + | 0.244224i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −41.5524 | + | 97.7757i | −0.0710298 | + | 0.167138i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −617.569 | − | 617.569i | −1.05208 | − | 1.05208i | −0.998567 | − | 0.0535098i | \(-0.982959\pi\) |
−0.0535098 | − | 0.998567i | \(-0.517041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 57.7316i | − | 0.0980163i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 430.761 | + | 430.761i | 0.728868 | + | 0.728868i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.7807 | − | 24.7807i | 0.0417887 | − | 0.0417887i | −0.685904 | − | 0.727692i | \(-0.740593\pi\) |
0.727692 | + | 0.685904i | \(0.240593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 310.690i | − | 0.522167i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 423.553i | 0.709470i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1084.86 | −1.81112 | −0.905559 | − | 0.424221i | \(-0.860548\pi\) | ||||
−0.905559 | + | 0.424221i | \(0.860548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1048.67 | −1.74488 | −0.872439 | − | 0.488723i | \(-0.837463\pi\) | ||||
−0.872439 | + | 0.488723i | \(0.837463\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.0982 | − | 20.0982i | −0.0333303 | − | 0.0333303i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −52.8580 | + | 52.8580i | −0.0873686 | + | 0.0873686i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 362.335 | 0.596927 | 0.298464 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298464 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.8544 | − | 32.8544i | 0.0539481 | − | 0.0539481i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 415.198 | + | 176.450i | 0.679538 | + | 0.288788i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 79.3587 | + | 79.3587i | 0.129459 | + | 0.129459i | 0.768868 | − | 0.639408i | \(-0.220821\pi\) |
−0.639408 | + | 0.768868i | \(0.720821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.2069i | 0.0296047i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −663.590 | − | 663.590i | −1.07551 | − | 1.07551i | −0.996906 | − | 0.0786054i | \(-0.974953\pi\) |
−0.0786054 | − | 0.996906i | \(-0.525047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 656.750 | − | 656.750i | 1.06098 | − | 1.06098i | 0.0629695 | − | 0.998015i | \(-0.479943\pi\) |
0.998015 | − | 0.0629695i | \(-0.0200571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 186.387i | − | 0.300140i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 502.869i | − | 0.807173i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −123.522 | −0.197635 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.8781 | 0.0476525 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 625.009 | + | 625.009i | 0.993655 | + | 0.993655i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 567.649 | − | 567.649i | 0.899602 | − | 0.899602i | −0.0957989 | − | 0.995401i | \(-0.530541\pi\) |
0.995401 | + | 0.0957989i | \(0.0305406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.0079 | 0.0647835 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −239.805 | + | 239.805i | −0.377646 | + | 0.377646i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −280.930 | + | 113.364i | −0.441020 | + | 0.177965i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 107.273 | + | 107.273i | 0.167876 | + | 0.167876i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 157.873i | 0.246292i | 0.992389 | + | 0.123146i | \(0.0392984\pi\) | ||||
−0.992389 | + | 0.123146i | \(0.960702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −288.261 | − | 288.261i | −0.448306 | − | 0.448306i | 0.446485 | − | 0.894791i | \(-0.352676\pi\) |
−0.894791 | + | 0.446485i | \(0.852676\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −178.488 | + | 178.488i | −0.276725 | + | 0.276725i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1079.96i | − | 1.66918i | −0.550875 | − | 0.834588i | \(-0.685706\pi\) | ||
0.550875 | − | 0.834588i | \(-0.314294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 527.996i | − | 0.813553i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −284.226 | −0.436599 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 757.451 | 1.15996 | 0.579978 | − | 0.814632i | \(-0.303061\pi\) | ||||
0.579978 | + | 0.814632i | \(0.303061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 474.149 | + | 474.149i | 0.723892 | + | 0.723892i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 204.293 | − | 204.293i | 0.310948 | − | 0.310948i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7089 | −0.0299072 | −0.0149536 | − | 0.999888i | \(-0.504760\pi\) | ||||
−0.0149536 | + | 0.999888i | \(0.504760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 381.567 | − | 381.567i | 0.577258 | − | 0.577258i | −0.356889 | − | 0.934147i | \(-0.616163\pi\) |
0.934147 | + | 0.356889i | \(0.116163\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 469.799 | − | 189.579i | 0.708596 | − | 0.285941i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.4138 | − | 17.4138i | −0.0261862 | − | 0.0261862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 189.820i | 0.284587i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −236.613 | − | 236.613i | −0.353682 | − | 0.353682i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −135.084 | + | 135.084i | −0.201317 | + | 0.201317i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 984.504i | − | 1.46286i | −0.681917 | − | 0.731429i | \(-0.738854\pi\) | ||
0.681917 | − | 0.731429i | \(-0.261146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 91.3454i | 0.135327i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −473.501 | −0.699411 | −0.349705 | − | 0.936860i | \(-0.613718\pi\) | ||||
−0.349705 | + | 0.936860i | \(0.613718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −827.591 | −1.21884 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −377.756 | − | 377.756i | −0.554708 | − | 0.554708i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −266.970 | + | 266.970i | −0.390879 | + | 0.390879i | −0.875001 | − | 0.484122i | \(-0.839139\pi\) |
0.484122 | + | 0.875001i | \(0.339139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −409.161 | −0.597316 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −60.6971 | + | 60.6971i | −0.0883509 | + | 0.0883509i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 101.272 | + | 250.965i | 0.146984 | + | 0.364245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 353.770 | + | 353.770i | 0.511968 | + | 0.511968i | 0.915129 | − | 0.403161i | \(-0.132088\pi\) |
−0.403161 | + | 0.915129i | \(0.632088\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 147.097i | − | 0.212261i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −104.198 | − | 104.198i | −0.149925 | − | 0.149925i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.3917 | − | 61.3917i | 0.0880800 | − | 0.0880800i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 76.9590i | − | 0.110099i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 59.3419i | 0.0846532i | 0.999104 | + | 0.0423266i | \(0.0134770\pi\) | ||||
−0.999104 | + | 0.0423266i | \(0.986523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 70.0623 | 0.0996619 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −163.736 | −0.232249 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −131.372 | − | 131.372i | −0.185816 | − | 0.185816i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −442.641 | + | 442.641i | −0.624317 | + | 0.624317i | −0.946632 | − | 0.322315i | \(-0.895539\pi\) |
0.322315 | + | 0.946632i | \(0.395539\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.0582 | 0.0155530 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 821.072 | − | 821.072i | 1.15157 | − | 1.15157i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −128.180 | − | 317.647i | −0.179273 | − | 0.444261i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 231.982 | + | 231.982i | 0.323545 | + | 0.323545i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 567.348i | 0.789079i | 0.918879 | + | 0.394539i | \(0.129096\pi\) | ||||
−0.918879 | + | 0.394539i | \(0.870904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −467.377 | − | 467.377i | −0.648234 | − | 0.648234i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 200.093 | − | 200.093i | 0.276753 | − | 0.276753i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 93.0278i | − | 0.128314i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 714.512i | 0.982823i | 0.870928 | + | 0.491411i | \(0.163519\pi\) | ||||
−0.870928 | + | 0.491411i | \(0.836481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1203.68 | 1.64663 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 592.536 | + | 592.536i | 0.808371 | + | 0.808371i | 0.984387 | − | 0.176016i | \(-0.0563210\pi\) |
−0.176016 | + | 0.984387i | \(0.556321\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 77.7461 | − | 77.7461i | 0.105777 | − | 0.105777i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 91.6415 | 0.124344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 116.248 | − | 116.248i | 0.157304 | − | 0.157304i | −0.624067 | − | 0.781371i | \(-0.714521\pi\) |
0.781371 | + | 0.624067i | \(0.214521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.7061 | − | 36.9575i | 0.0211958 | − | 0.0498751i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −207.488 | − | 207.488i | −0.279257 | − | 0.279257i | 0.553555 | − | 0.832812i | \(-0.313271\pi\) |
−0.832812 | + | 0.553555i | \(0.813271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 614.134i | − | 0.824341i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −122.451 | − | 122.451i | −0.163924 | − | 0.163924i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −584.058 | + | 584.058i | −0.779784 | + | 0.779784i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1278.85i | − | 1.70286i | −0.524470 | − | 0.851429i | \(-0.675736\pi\) | ||
0.524470 | − | 0.851429i | \(-0.324264\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 659.051i | − | 0.875234i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 72.7137 | 0.0963095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −271.889 | −0.359166 | −0.179583 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179583 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 424.934 | + | 424.934i | 0.559860 | + | 0.559860i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −62.5106 | + | 62.5106i | −0.0821427 | + | 0.0821427i | −0.746984 | − | 0.664842i | \(-0.768499\pi\) |
0.664842 | + | 0.746984i | \(0.268499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 703.361 | 0.921836 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −130.015 | + | 130.015i | −0.169954 | + | 0.169954i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −653.100 | − | 277.553i | −0.851499 | − | 0.361868i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 595.694 | + | 595.694i | 0.774635 | + | 0.774635i | 0.978913 | − | 0.204278i | \(-0.0654847\pi\) |
−0.204278 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 508.996i | − | 0.660177i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −583.166 | − | 583.166i | −0.754419 | − | 0.754419i | 0.220881 | − | 0.975301i | \(-0.429107\pi\) |
−0.975301 | + | 0.220881i | \(0.929107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −402.395 | + | 402.395i | −0.519219 | + | 0.519219i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 344.933i | − | 0.443929i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 6.88189i | − | 0.00883426i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −489.132 | −0.626289 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.4973 | −0.0351179 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 511.942 | + | 511.942i | 0.652156 | + | 0.652156i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 969.877 | − | 969.877i | 1.23237 | − | 1.23237i | 0.269322 | − | 0.963050i | \(-0.413200\pi\) |
0.963050 | − | 0.269322i | \(-0.0867997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −272.712 | −0.345643 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.1253 | − | 96.1253i | 0.121524 | − | 0.121524i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 96.0811 | + | 238.101i | 0.121162 | + | 0.300253i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −69.4534 | − | 69.4534i | −0.0873628 | − | 0.0873628i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1347.04i | 1.69014i | 0.534659 | + | 0.845068i | \(0.320440\pi\) | ||||
−0.534659 | + | 0.845068i | \(0.679560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 552.099 | + | 552.099i | 0.690988 | + | 0.690988i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −210.436 | + | 210.436i | −0.262717 | + | 0.262717i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 931.511i | 1.16004i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 495.327i | − | 0.615314i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −302.656 | −0.375039 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1087.83 | −1.34465 | −0.672327 | − | 0.740254i | \(-0.734705\pi\) | ||||
−0.672327 | + | 0.740254i | \(0.734705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −703.042 | − | 703.042i | −0.866882 | − | 0.866882i | 0.125244 | − | 0.992126i | \(-0.460029\pi\) |
−0.992126 | + | 0.125244i | \(0.960029\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.4856 | + | 27.4856i | −0.0338076 | + | 0.0338076i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 441.092 | 0.541217 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67.4652 | − | 67.4652i | 0.0825768 | − | 0.0825768i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −181.950 | − | 77.3247i | −0.222161 | − | 0.0944135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 695.520 | + | 695.520i | 0.847162 | + | 0.847162i | 0.989778 | − | 0.142616i | \(-0.0455515\pi\) |
−0.142616 | + | 0.989778i | \(0.545552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 770.965i | 0.936774i | 0.883523 | + | 0.468387i | \(0.155165\pi\) | ||||
−0.883523 | + | 0.468387i | \(0.844835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −208.253 | − | 208.253i | −0.252428 | − | 0.252428i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1073.08 | + | 1073.08i | −1.29756 | + | 1.29756i | −0.367555 | + | 0.930002i | \(0.619805\pi\) |
−0.930002 | + | 0.367555i | \(0.880195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 718.597i | 0.866824i | 0.901196 | + | 0.433412i | \(0.142691\pi\) | ||||
−0.901196 | + | 0.433412i | \(0.857309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 417.567i | 0.502488i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −524.303 | −0.629415 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 589.251 | 0.705690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 118.940 | + | 118.940i | 0.142103 | + | 0.142103i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 77.4498 | − | 77.4498i | 0.0923121 | − | 0.0923121i | −0.659443 | − | 0.751755i | \(-0.729208\pi\) |
0.751755 | + | 0.659443i | \(0.229208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −812.996 | −0.966702 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 258.140 | − | 258.140i | 0.306216 | − | 0.306216i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −460.291 | − | 8.42640i | −0.544723 | − | 0.00997207i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −98.3631 | − | 98.3631i | −0.116131 | − | 0.116131i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 607.594i | − | 0.715658i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 996.442 | + | 996.442i | 1.17091 | + | 1.17091i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −294.965 | + | 294.965i | −0.345797 | + | 0.345797i | −0.858541 | − | 0.512744i | \(-0.828629\pi\) |
0.512744 | + | 0.858541i | \(0.328629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.5744i | 0.0170461i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1291.93i | 1.50750i | 0.657161 | + | 0.753751i | \(0.271757\pi\) | ||||
−0.657161 | + | 0.753751i | \(0.728243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −770.932 | −0.897476 | −0.448738 | − | 0.893663i | \(-0.648126\pi\) | ||||
−0.448738 | + | 0.893663i | \(0.648126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.8811 | −0.0393509 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 854.917 | + | 854.917i | 0.990634 | + | 0.990634i | 0.999957 | − | 0.00932255i | \(-0.00296750\pi\) |
−0.00932255 | + | 0.999957i | \(0.502968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 469.554 | − | 469.554i | 0.542837 | − | 0.542837i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 376.229 | 0.433944 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.2109 | + | 25.2109i | −0.0290114 | + | 0.0290114i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.1734 | − | 113.355i | 0.0553081 | − | 0.130144i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 346.323 | + | 346.323i | 0.396705 | + | 0.396705i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 587.975i | 0.671971i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −333.435 | − | 333.435i | −0.380199 | − | 0.380199i | 0.490975 | − | 0.871174i | \(-0.336641\pi\) |
−0.871174 | + | 0.490975i | \(0.836641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 605.630 | − | 605.630i | 0.688999 | − | 0.688999i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 297.062i | 0.337187i | 0.985686 | + | 0.168593i | \(0.0539225\pi\) | ||||
−0.985686 | + | 0.168593i | \(0.946078\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1112.56i | 1.25998i | 0.776603 | + | 0.629990i | \(0.216941\pi\) | ||||
−0.776603 | + | 0.629990i | \(0.783059\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 257.554 | 0.291021 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.2311 | −0.0307003 | −0.0153501 | − | 0.999882i | \(-0.504886\pi\) | ||||
−0.0153501 | + | 0.999882i | \(0.504886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −446.252 | − | 446.252i | −0.501971 | − | 0.501971i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −61.5558 | + | 61.5558i | −0.0690862 | + | 0.0690862i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.8892 | 0.0693048 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −167.320 | + | 167.320i | −0.186950 | + | 0.186950i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 748.994 | − | 302.242i | 0.834998 | − | 0.336948i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −121.131 | − | 121.131i | −0.134740 | − | 0.134740i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 468.379i | 0.519843i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −332.147 | − | 332.147i | −0.367826 | − | 0.367826i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 324.281 | − | 324.281i | 0.358322 | − | 0.358322i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 183.412i | − | 0.202219i | −0.994875 | − | 0.101109i | \(-0.967761\pi\) | ||
0.994875 | − | 0.101109i | \(-0.0322392\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 109.951i | 0.120958i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 506.343 | 0.555810 | 0.277905 | − | 0.960609i | \(-0.410360\pi\) | ||||
0.277905 | + | 0.960609i | \(0.410360\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 558.339 | 0.611544 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −65.8933 | − | 65.8933i | −0.0720146 | − | 0.0720146i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −882.341 | + | 882.341i | −0.962204 | + | 0.962204i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 195.184 | 0.212388 | 0.106194 | − | 0.994345i | \(-0.466134\pi\) | ||||
0.106194 | + | 0.994345i | \(0.466134\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −687.876 | + | 687.876i | −0.746879 | + | 0.746879i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −257.123 | + | 605.027i | −0.278573 | + | 0.655501i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −488.341 | − | 488.341i | −0.527936 | − | 0.527936i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 391.168i | 0.421972i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −636.021 | − | 636.021i | −0.684630 | − | 0.684630i | 0.276410 | − | 0.961040i | \(-0.410855\pi\) |
−0.961040 | + | 0.276410i | \(0.910855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.3866 | + | 29.3866i | −0.0315646 | + | 0.0315646i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 273.442i | 0.293078i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 592.827i | − | 0.634040i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 159.058 | 0.169752 | 0.0848761 | − | 0.996392i | \(-0.472951\pi\) | ||||
0.0848761 | + | 0.996392i | \(0.472951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −151.339 | −0.161170 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 667.783 | + | 667.783i | 0.709652 | + | 0.709652i | 0.966462 | − | 0.256810i | \(-0.0826714\pi\) |
−0.256810 | + | 0.966462i | \(0.582671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 97.8759 | − | 97.8759i | 0.103792 | − | 0.103792i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 71.7531 | 0.0759292 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −370.339 | + | 370.339i | −0.391065 | + | 0.391065i | −0.875067 | − | 0.484002i | \(-0.839183\pi\) |
0.484002 | + | 0.875067i | \(0.339183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1152.22 | + | 489.669i | 1.21415 | + | 0.515985i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −608.972 | − | 608.972i | −0.640349 | − | 0.640349i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1343.91i | − | 1.41019i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) | ||
0.709113 | − | 0.705095i | \(-0.249096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 627.752 | + | 627.752i | 0.657332 | + | 0.657332i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 62.6896 | − | 62.6896i | 0.0655063 | − | 0.0655063i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 761.406i | − | 0.793958i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 86.9137i | 0.0904409i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 488.823 | 0.507605 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −890.383 | −0.922677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −629.403 | − | 629.403i | −0.650882 | − | 0.650882i | 0.302323 | − | 0.953205i | \(-0.402238\pi\) |
−0.953205 | + | 0.302323i | \(0.902238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.1433 | − | 49.1433i | 0.0507155 | − | 0.0507155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.3706 | −0.0147998 | −0.00739990 | − | 0.999973i | \(-0.502355\pi\) | ||||
−0.00739990 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 193.902 | − | 193.902i | 0.199282 | − | 0.199282i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −367.070 | + | 148.124i | −0.376482 | + | 0.151922i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −674.932 | − | 674.932i | −0.690821 | − | 0.690821i | 0.271592 | − | 0.962413i | \(-0.412450\pi\) |
−0.962413 | + | 0.271592i | \(0.912450\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 959.525i | − | 0.980107i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −294.337 | − | 294.337i | −0.300038 | − | 0.300038i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −255.689 | + | 255.689i | −0.260110 | + | 0.260110i | −0.825099 | − | 0.564988i | \(-0.808881\pi\) |
0.564988 | + | 0.825099i | \(0.308881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 958.096i | − | 0.972687i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 304.695i | − | 0.308708i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1919.01 | 1.94036 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −785.926 | −0.793063 | −0.396532 | − | 0.918021i | \(-0.629786\pi\) | ||||
−0.396532 | + | 0.918021i | \(0.629786\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 117.114 | + | 117.114i | 0.117939 | + | 0.117939i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 471.033 | − | 471.033i | 0.473400 | − | 0.473400i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 361.986 | 0.363075 | 0.181538 | − | 0.983384i | \(-0.441893\pi\) | ||||
0.181538 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −144.345 | + | 144.345i | −0.144489 | + | 0.144489i |
(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 | 156.3.j.a.73.2 | ✓ | 8 | |
3.2 | odd | 2 | 468.3.m.d.73.2 | 8 | |||
4.3 | odd | 2 | 624.3.ba.d.385.4 | 8 | |||
13.5 | odd | 4 | inner | 156.3.j.a.109.2 | yes | 8 | |
39.5 | even | 4 | 468.3.m.d.109.2 | 8 | |||
52.31 | even | 4 | 624.3.ba.d.577.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.j.a.73.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
156.3.j.a.109.2 | yes | 8 | 13.5 | odd | 4 | inner | |
468.3.m.d.73.2 | 8 | 3.2 | odd | 2 | |||
468.3.m.d.109.2 | 8 | 39.5 | even | 4 | |||
624.3.ba.d.385.4 | 8 | 4.3 | odd | 2 | |||
624.3.ba.d.577.4 | 8 | 52.31 | even | 4 |