Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.4 | ||
Root | \(4.17259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.1801 |
Dual form | 2520.2.bi.s.361.4 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.835066 | + | 2.51051i | 0.315625 | + | 0.948884i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.11357 | − | 5.39287i | −0.938777 | − | 1.62601i | −0.767755 | − | 0.640743i | \(-0.778626\pi\) |
−0.171022 | − | 0.985267i | \(-0.554707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.77007 | −1.04563 | −0.522815 | − | 0.852446i | \(-0.675118\pi\) | ||||
−0.522815 | + | 0.852446i | \(0.675118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.313192 | − | 0.542464i | −0.0759602 | − | 0.131567i | 0.825543 | − | 0.564339i | \(-0.190869\pi\) |
−0.901503 | + | 0.432772i | \(0.857536\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.206663 | + | 0.357951i | −0.0474117 | + | 0.0821196i | −0.888757 | − | 0.458378i | \(-0.848431\pi\) |
0.841346 | + | 0.540497i | \(0.181764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.04173 | + | 3.53638i | −0.425730 | + | 0.737386i | −0.996488 | − | 0.0837323i | \(-0.973316\pi\) |
0.570758 | + | 0.821118i | \(0.306649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.12720 | 0.766403 | 0.383201 | − | 0.923665i | \(-0.374822\pi\) | ||||
0.383201 | + | 0.923665i | \(0.374822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32848 | + | 7.49714i | 0.777418 | + | 1.34653i | 0.933426 | + | 0.358771i | \(0.116804\pi\) |
−0.156008 | + | 0.987756i | \(0.549863\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.59170 | + | 0.532067i | 0.438077 | + | 0.0899358i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.59170 | + | 6.22101i | −0.590472 | + | 1.02273i | 0.403697 | + | 0.914893i | \(0.367725\pi\) |
−0.994169 | + | 0.107834i | \(0.965608\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.88688 | −0.763203 | −0.381601 | − | 0.924327i | \(-0.624627\pi\) | ||||
−0.381601 | + | 0.924327i | \(0.624627\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6236 | −1.62008 | −0.810042 | − | 0.586372i | \(-0.800556\pi\) | ||||
−0.810042 | + | 0.586372i | \(0.800556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49861 | + | 9.52387i | −0.802055 | + | 1.38920i | 0.116207 | + | 0.993225i | \(0.462926\pi\) |
−0.918262 | + | 0.395974i | \(0.870407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.60533 | + | 4.19288i | −0.800762 | + | 0.598983i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.271463 | + | 0.470188i | 0.0372884 | + | 0.0645853i | 0.884067 | − | 0.467360i | \(-0.154795\pi\) |
−0.846779 | + | 0.531945i | \(0.821461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.22715 | −0.839668 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.16354 | + | 7.21147i | 0.542047 | + | 0.938853i | 0.998786 | + | 0.0492526i | \(0.0156839\pi\) |
−0.456739 | + | 0.889601i | \(0.650983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.963468 | − | 1.66878i | 0.123359 | − | 0.213665i | −0.797731 | − | 0.603013i | \(-0.793967\pi\) |
0.921090 | + | 0.389349i | \(0.127300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.88504 | + | 3.26498i | −0.233810 | + | 0.404971i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50520 | − | 6.07118i | −0.428228 | − | 0.741713i | 0.568488 | − | 0.822692i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809791i | \(0.974195\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3271 | 1.46296 | 0.731478 | − | 0.681865i | \(-0.238831\pi\) | ||||
0.731478 | + | 0.681865i | \(0.238831\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.58548 | − | 4.47818i | −0.302607 | − | 0.524131i | 0.674119 | − | 0.738623i | \(-0.264524\pi\) |
−0.976726 | + | 0.214492i | \(0.931190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.9388 | − | 12.3201i | 1.24659 | − | 1.40400i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.57807 | + | 6.19739i | −0.402564 | + | 0.697261i | −0.994035 | − | 0.109065i | \(-0.965214\pi\) |
0.591471 | + | 0.806327i | \(0.298548\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0541 | −1.10359 | −0.551793 | − | 0.833981i | \(-0.686056\pi\) | ||||
−0.551793 | + | 0.833981i | \(0.686056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.626384 | −0.0679409 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60653 | − | 2.78259i | 0.170292 | − | 0.294954i | −0.768230 | − | 0.640174i | \(-0.778862\pi\) |
0.938522 | + | 0.345220i | \(0.112196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.14826 | − | 9.46481i | −0.330027 | − | 0.992181i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.206663 | + | 0.357951i | 0.0212032 | + | 0.0367250i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7007 | 1.39110 | 0.695548 | − | 0.718480i | \(-0.255162\pi\) | ||||
0.695548 | + | 0.718480i | \(0.255162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.67681 | − | 13.2966i | −0.763871 | − | 1.32306i | −0.940841 | − | 0.338847i | \(-0.889963\pi\) |
0.176970 | − | 0.984216i | \(-0.443370\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.72513 | + | 9.91621i | −0.564114 | + | 0.977073i | 0.433018 | + | 0.901385i | \(0.357449\pi\) |
−0.997132 | + | 0.0756880i | \(0.975885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.31319 | + | 2.27452i | −0.126951 | + | 0.219886i | −0.922494 | − | 0.386012i | \(-0.873852\pi\) |
0.795543 | + | 0.605897i | \(0.207186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19200 | − | 3.79666i | −0.209956 | − | 0.363654i | 0.741744 | − | 0.670683i | \(-0.233999\pi\) |
−0.951700 | + | 0.307028i | \(0.900665\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.34026 | −0.502370 | −0.251185 | − | 0.967939i | \(-0.580820\pi\) | ||||
−0.251185 | + | 0.967939i | \(0.580820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.04173 | + | 3.53638i | 0.190392 | + | 0.329769i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.10033 | − | 1.23927i | 0.100867 | − | 0.113603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.8887 | + | 24.0559i | −1.26261 | + | 2.18690i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.0510 | −1.86798 | −0.933988 | − | 0.357305i | \(-0.883696\pi\) | ||||
−0.933988 | + | 0.357305i | \(0.883696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04997 | − | 1.81860i | 0.0917363 | − | 0.158892i | −0.816505 | − | 0.577338i | \(-0.804092\pi\) |
0.908242 | + | 0.418446i | \(0.137425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07122 | − | 0.219917i | −0.0928863 | − | 0.0190693i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.64028 | − | 9.76925i | −0.481882 | − | 0.834643i | 0.517902 | − | 0.855440i | \(-0.326713\pi\) |
−0.999784 | + | 0.0207966i | \(0.993380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.70348 | 0.314125 | 0.157063 | − | 0.987589i | \(-0.449798\pi\) | ||||
0.157063 | + | 0.987589i | \(0.449798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.7384 | + | 20.3315i | 0.981614 | + | 1.70020i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.06360 | − | 3.57426i | 0.171373 | − | 0.296826i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.26686 | − | 12.5866i | 0.595324 | − | 1.03113i | −0.398177 | − | 0.917309i | \(-0.630357\pi\) |
0.993501 | − | 0.113823i | \(-0.0363096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.93381 | + | 5.08151i | 0.238750 | + | 0.413527i | 0.960356 | − | 0.278777i | \(-0.0899290\pi\) |
−0.721606 | + | 0.692304i | \(0.756596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.65696 | 0.695343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.46330 | + | 7.73066i | 0.356210 | + | 0.616974i | 0.987324 | − | 0.158716i | \(-0.0507355\pi\) |
−0.631114 | + | 0.775690i | \(0.717402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5831 | − | 2.17267i | −0.834065 | − | 0.171231i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.78694 | + | 8.29123i | −0.374942 | + | 0.649419i | −0.990318 | − | 0.138815i | \(-0.955671\pi\) |
0.615376 | + | 0.788234i | \(0.289004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.08346 | 0.161223 | 0.0806114 | − | 0.996746i | \(-0.474313\pi\) | ||||
0.0806114 | + | 0.996746i | \(0.474313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.21344 | 0.0933419 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.39867 | + | 2.42256i | −0.106339 | + | 0.184184i | −0.914284 | − | 0.405073i | \(-0.867246\pi\) |
0.807946 | + | 0.589257i | \(0.200579\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.75663 | − | 1.97844i | 0.132789 | − | 0.149556i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.23337 | + | 10.7965i | 0.465904 | + | 0.806969i | 0.999242 | − | 0.0389331i | \(-0.0123959\pi\) |
−0.533338 | + | 0.845902i | \(0.679063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.2316 | −1.94978 | −0.974891 | − | 0.222683i | \(-0.928518\pi\) | ||||
−0.974891 | + | 0.222683i | \(0.928518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.59170 | + | 6.22101i | 0.264067 | + | 0.457377i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.95029 | + | 3.37801i | −0.142619 | + | 0.247024i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.29652 | − | 5.70973i | 0.238527 | − | 0.413142i | −0.721764 | − | 0.692139i | \(-0.756669\pi\) |
0.960292 | + | 0.278997i | \(0.0900020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.05500 | + | 3.55936i | 0.147922 | + | 0.256208i | 0.930459 | − | 0.366395i | \(-0.119408\pi\) |
−0.782537 | + | 0.622604i | \(0.786075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5170 | −0.749302 | −0.374651 | − | 0.927166i | \(-0.622238\pi\) | ||||
−0.374651 | + | 0.927166i | \(0.622238\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.08028 | + | 3.60315i | 0.147467 | + | 0.255420i | 0.930291 | − | 0.366823i | \(-0.119555\pi\) |
−0.782824 | + | 0.622244i | \(0.786221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.44649 | + | 10.3614i | 0.241896 | + | 0.727227i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44344 | + | 4.23216i | −0.170657 | + | 0.295587i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.57384 | 0.178036 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3230 | 0.710668 | 0.355334 | − | 0.934739i | \(-0.384367\pi\) | ||||
0.355334 | + | 0.934739i | \(0.384367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.31180 | + | 9.20031i | −0.362262 | + | 0.627456i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.2071 | + | 17.1273i | −1.03233 | + | 1.16268i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18076 | + | 2.04513i | 0.0794263 | + | 0.137570i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8804 | 1.53219 | 0.766093 | − | 0.642730i | \(-0.222198\pi\) | ||||
0.766093 | + | 0.642730i | \(0.222198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.14388 | − | 7.17741i | −0.275039 | − | 0.476382i | 0.695106 | − | 0.718907i | \(-0.255357\pi\) |
−0.970145 | + | 0.242526i | \(0.922024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8521 | + | 20.5285i | −0.783211 | + | 1.35656i | 0.146850 | + | 0.989159i | \(0.453086\pi\) |
−0.930062 | + | 0.367403i | \(0.880247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.59672 | + | 11.4259i | −0.432166 | + | 0.748533i | −0.997060 | − | 0.0766306i | \(-0.975584\pi\) |
0.564894 | + | 0.825164i | \(0.308917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.49861 | + | 9.52387i | 0.358690 | + | 0.621269i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9086 | −1.48183 | −0.740916 | − | 0.671597i | \(-0.765609\pi\) | ||||
−0.740916 | + | 0.671597i | \(0.765609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.60173 | − | 16.6307i | −0.618502 | − | 1.07128i | −0.989759 | − | 0.142746i | \(-0.954407\pi\) |
0.371258 | − | 0.928530i | \(-0.378927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.828478 | + | 6.95080i | 0.0529295 | + | 0.444070i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.779134 | − | 1.34950i | 0.0495751 | − | 0.0858667i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.2255 | −0.708548 | −0.354274 | − | 0.935142i | \(-0.615272\pi\) | ||||
−0.354274 | + | 0.935142i | \(0.615272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4283 | 1.59866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.89747 | − | 15.4109i | 0.555009 | − | 0.961304i | −0.442894 | − | 0.896574i | \(-0.646048\pi\) |
0.997903 | − | 0.0647296i | \(-0.0206185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.6172 | − | 3.82205i | −1.15682 | − | 0.237491i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0238 | + | 26.0219i | 0.926404 | + | 1.60458i | 0.789287 | + | 0.614024i | \(0.210450\pi\) |
0.137117 | + | 0.990555i | \(0.456216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.542927 | 0.0333517 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.8404 | − | 22.2401i | −0.782890 | − | 1.35601i | −0.930251 | − | 0.366923i | \(-0.880411\pi\) |
0.147361 | − | 0.989083i | \(-0.452922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.67700 | − | 16.7611i | 0.587836 | − | 1.01816i | −0.406679 | − | 0.913571i | \(-0.633313\pi\) |
0.994515 | − | 0.104591i | \(-0.0333533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.11357 | + | 5.39287i | −0.187755 | + | 0.325202i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6558 | − | 27.1166i | −0.940663 | − | 1.62928i | −0.764210 | − | 0.644968i | \(-0.776871\pi\) |
−0.176453 | − | 0.984309i | \(-0.556462\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.78621 | −0.225866 | −0.112933 | − | 0.993603i | \(-0.536025\pi\) | ||||
−0.112933 | + | 0.993603i | \(0.536025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.26805 | + | 16.0527i | 0.550929 | + | 0.954236i | 0.998208 | + | 0.0598420i | \(0.0190597\pi\) |
−0.447279 | + | 0.894394i | \(0.647607\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.08087 | − | 12.2686i | −0.240886 | − | 0.724191i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.30382 | − | 14.3826i | 0.488460 | − | 0.846038i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.1048 | 1.70032 | 0.850161 | − | 0.526523i | \(-0.176505\pi\) | ||||
0.850161 | + | 0.526523i | \(0.176505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.32709 | 0.484822 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.69746 | − | 13.3324i | 0.445156 | − | 0.771033i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.87140 | − | 26.6707i | −0.511339 | − | 1.53727i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.963468 | − | 1.66878i | −0.0551680 | − | 0.0955538i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0120 | 0.799709 | 0.399855 | − | 0.916579i | \(-0.369061\pi\) | ||||
0.399855 | + | 0.916579i | \(0.369061\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.88020 | + | 6.72071i | 0.220026 | + | 0.381097i | 0.954816 | − | 0.297199i | \(-0.0960524\pi\) |
−0.734789 | + | 0.678295i | \(0.762719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.09874 | − | 10.5633i | 0.344721 | − | 0.597075i | −0.640582 | − | 0.767890i | \(-0.721307\pi\) |
0.985303 | + | 0.170815i | \(0.0546401\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.45284 | − | 4.24845i | 0.137765 | − | 0.238617i | −0.788885 | − | 0.614541i | \(-0.789341\pi\) |
0.926650 | + | 0.375924i | \(0.122675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8504 | − | 22.2575i | −0.719482 | − | 1.24618i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.258901 | 0.0144056 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.88504 | + | 3.26498i | 0.104563 | + | 0.181108i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.5015 | − | 5.85126i | −1.57134 | − | 0.322590i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.65686 | + | 9.79798i | −0.310929 | + | 0.538545i | −0.978564 | − | 0.205944i | \(-0.933974\pi\) |
0.667634 | + | 0.744489i | \(0.267307\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.01039 | −0.383019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8091 | 0.915647 | 0.457824 | − | 0.889043i | \(-0.348629\pi\) | ||||
0.457824 | + | 0.889043i | \(0.348629\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.9541 | − | 46.6858i | 1.45964 | − | 2.52818i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2071 | − | 10.5709i | −0.821106 | − | 0.570776i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.93938 | − | 6.82321i | −0.211477 | − | 0.366289i | 0.740700 | − | 0.671836i | \(-0.234494\pi\) |
−0.952177 | + | 0.305547i | \(0.901161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2472 | 1.56557 | 0.782783 | − | 0.622294i | \(-0.213799\pi\) | ||||
0.782783 | + | 0.622294i | \(0.213799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.51380 | − | 7.81814i | −0.240246 | − | 0.416117i | 0.720539 | − | 0.693415i | \(-0.243895\pi\) |
−0.960784 | + | 0.277297i | \(0.910561\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.16354 | − | 10.6756i | 0.327127 | − | 0.566600i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0302 | + | 20.8370i | −0.634932 | + | 1.09973i | 0.351597 | + | 0.936151i | \(0.385639\pi\) |
−0.986529 | + | 0.163584i | \(0.947695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.41458 | + | 16.3065i | 0.495504 | + | 0.858239i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.17095 | −0.270660 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.25183 | − | 12.5605i | −0.378543 | − | 0.655655i | 0.612308 | − | 0.790619i | \(-0.290241\pi\) |
−0.990850 | + | 0.134964i | \(0.956908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.953723 | + | 1.07415i | −0.0495148 | + | 0.0557671i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.5654 | + | 18.2999i | −0.547057 | + | 0.947531i | 0.451417 | + | 0.892313i | \(0.350919\pi\) |
−0.998474 | + | 0.0552177i | \(0.982415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.5599 | −0.801373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.96626 | 0.255100 | 0.127550 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127550 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.08125 | + | 12.2651i | −0.361835 | + | 0.626716i | −0.988263 | − | 0.152763i | \(-0.951183\pi\) |
0.626428 | + | 0.779479i | \(0.284516\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.20007 | − | 15.6333i | −0.265020 | − | 0.796748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0905 | + | 20.9413i | 0.613012 | + | 1.06177i | 0.990730 | + | 0.135847i | \(0.0433755\pi\) |
−0.377718 | + | 0.925921i | \(0.623291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.55781 | 0.129354 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.57807 | + | 6.19739i | 0.180032 | + | 0.311825i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.29935 | + | 7.44670i | −0.215778 | + | 0.373739i | −0.953513 | − | 0.301352i | \(-0.902562\pi\) |
0.737735 | + | 0.675091i | \(0.235896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0909 | − | 33.0665i | 0.953356 | − | 1.65126i | 0.215269 | − | 0.976555i | \(-0.430937\pi\) |
0.738087 | − | 0.674706i | \(-0.235730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.3187 | − | 28.2648i | −0.812891 | − | 1.40797i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.7321 | 2.21729 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.21167 | + | 12.4910i | 0.356594 | + | 0.617639i | 0.987389 | − | 0.158310i | \(-0.0506046\pi\) |
−0.630795 | + | 0.775949i | \(0.717271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.6276 | + | 16.4747i | −0.719779 | + | 0.810666i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.02707 | + | 8.70714i | −0.246769 | + | 0.427417i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8929 | 0.532151 | 0.266075 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266075 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.95051 | 0.192536 | 0.0962679 | − | 0.995355i | \(-0.469309\pi\) | ||||
0.0962679 | + | 0.995355i | \(0.469309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.313192 | + | 0.542464i | −0.0151920 | + | 0.0263134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.99404 | + | 1.02526i | 0.241679 | + | 0.0496158i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3002 | − | 26.5007i | −0.736985 | − | 1.27650i | −0.953847 | − | 0.300293i | \(-0.902915\pi\) |
0.216862 | − | 0.976202i | \(-0.430418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8636 | 1.29098 | 0.645491 | − | 0.763768i | \(-0.276653\pi\) | ||||
0.645491 | + | 0.763768i | \(0.276653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.843900 | − | 1.46168i | −0.0403692 | − | 0.0699215i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.10312 | − | 14.0350i | 0.386741 | − | 0.669855i | −0.605268 | − | 0.796022i | \(-0.706934\pi\) |
0.992009 | + | 0.126167i | \(0.0402675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8070 | + | 22.1824i | −0.608479 | + | 1.05392i | 0.383012 | + | 0.923743i | \(0.374887\pi\) |
−0.991491 | + | 0.130173i | \(0.958447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.60653 | − | 2.78259i | −0.0761568 | − | 0.131907i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.3527 | −0.630153 | −0.315077 | − | 0.949066i | \(-0.602030\pi\) | ||||
−0.315077 | + | 0.949066i | \(0.602030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.2157 | + | 26.3543i | 0.716478 | + | 1.24098i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.77089 | − | 2.00593i | −0.458067 | − | 0.0940396i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.94506 | − | 5.10099i | 0.137764 | − | 0.238614i | −0.788886 | − | 0.614540i | \(-0.789342\pi\) |
0.926650 | + | 0.375925i | \(0.122675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.14635 | 0.332839 | 0.166419 | − | 0.986055i | \(-0.446779\pi\) | ||||
0.166419 | + | 0.986055i | \(0.446779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.97073 | 0.0915874 | 0.0457937 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457937 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2709 | + | 21.2538i | −0.567829 | + | 0.983509i | 0.428951 | + | 0.903328i | \(0.358883\pi\) |
−0.996780 | + | 0.0801813i | \(0.974450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.3147 | − | 13.8697i | 0.568640 | − | 0.640442i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.0774 | + | 57.2917i | 1.52090 | + | 2.63427i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.413326 | 0.0189647 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7071 | − | 25.4734i | −0.671983 | − | 1.16391i | −0.977341 | − | 0.211671i | \(-0.932110\pi\) |
0.305358 | − | 0.952237i | \(-0.401224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5410 | − | 23.4536i | 0.617415 | − | 1.06939i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.85035 | − | 11.8652i | 0.311058 | − | 0.538769i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3624 | − | 23.1444i | −0.605509 | − | 1.04877i | −0.991971 | − | 0.126467i | \(-0.959636\pi\) |
0.386462 | − | 0.922305i | \(-0.373697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9946 | −1.30851 | −0.654254 | − | 0.756275i | \(-0.727017\pi\) | ||||
−0.654254 | + | 0.756275i | \(0.727017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.29261 | − | 2.23886i | −0.0582161 | − | 0.100833i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2939 | + | 30.9473i | 0.461746 | + | 1.38818i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0424 | + | 27.7862i | −0.718154 | + | 1.24388i | 0.243576 | + | 0.969882i | \(0.421680\pi\) |
−0.961730 | + | 0.273998i | \(0.911654\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4528 | 1.17947 | 0.589737 | − | 0.807596i | \(-0.299232\pi\) | ||||
0.589737 | + | 0.807596i | \(0.299232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.3536 | −0.683227 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.38606 | − | 2.40073i | 0.0614361 | − | 0.106411i | −0.833671 | − | 0.552261i | \(-0.813765\pi\) |
0.895108 | + | 0.445850i | \(0.147099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.08347 | − | 10.2304i | 0.401829 | − | 0.452568i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.72513 | + | 9.91621i | 0.252279 | + | 0.436960i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 68.4813 | 3.01180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.216885 | − | 0.375656i | −0.00950190 | − | 0.0164578i | 0.861235 | − | 0.508206i | \(-0.169691\pi\) |
−0.870737 | + | 0.491749i | \(0.836358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3483 | − | 19.6559i | 0.496228 | − | 0.859492i | −0.503763 | − | 0.863842i | \(-0.668051\pi\) |
0.999991 | + | 0.00435014i | \(0.00138470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.71129 | − | 4.69609i | 0.118106 | − | 0.204565i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.16269 | + | 5.47794i | 0.137508 | + | 0.238171i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.4239 | 0.798028 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.31319 | + | 2.27452i | 0.0567742 | + | 0.0983359i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 40.0643 | + | 17.1740i | 1.72569 | + | 0.739735i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.52227 | − | 13.0290i | 0.323408 | − | 0.560158i | −0.657781 | − | 0.753209i | \(-0.728505\pi\) |
0.981189 | + | 0.193051i | \(0.0618382\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.38401 | −0.187790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5681 | 0.622889 | 0.311444 | − | 0.950264i | \(-0.399187\pi\) | ||||
0.311444 | + | 0.950264i | \(0.399187\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.852941 | + | 1.47734i | −0.0363365 | + | 0.0629366i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.5465 | − | 3.80755i | −0.788679 | − | 0.161913i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.66883 | − | 15.0149i | −0.367310 | − | 0.636200i | 0.621834 | − | 0.783149i | \(-0.286388\pi\) |
−0.989144 | + | 0.146949i | \(0.953055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0517 | 1.69401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.6108 | + | 21.8426i | 0.531482 | + | 0.920554i | 0.999325 | + | 0.0367425i | \(0.0116981\pi\) |
−0.467842 | + | 0.883812i | \(0.654969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.67013 | + | 4.62480i | −0.112333 | + | 0.194567i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.95671 | + | 10.3173i | −0.249718 | + | 0.432525i | −0.963448 | − | 0.267897i | \(-0.913671\pi\) |
0.713729 | + | 0.700422i | \(0.247005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.9693 | + | 32.8559i | 0.793842 | + | 1.37498i | 0.923572 | + | 0.383426i | \(0.125256\pi\) |
−0.129729 | + | 0.991549i | \(0.541411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.08346 | 0.170292 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.94540 | + | 15.4939i | 0.372402 | + | 0.645019i | 0.989934 | − | 0.141526i | \(-0.0452010\pi\) |
−0.617533 | + | 0.786545i | \(0.711868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.39587 | − | 25.2410i | −0.348319 | − | 1.04717i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.69044 | − | 2.92793i | 0.0700110 | − | 0.121263i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.76676 | 0.155471 | 0.0777355 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777355 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.57814 | −0.147435 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0905 | + | 31.3337i | −0.742889 | + | 1.28672i | 0.208285 | + | 0.978068i | \(0.433212\pi\) |
−0.951175 | + | 0.308654i | \(0.900122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.523072 | − | 1.57254i | −0.0214439 | − | 0.0644680i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7404 | − | 35.9234i | −0.847430 | − | 1.46779i | −0.883494 | − | 0.468443i | \(-0.844815\pi\) |
0.0360636 | − | 0.999349i | \(-0.488518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.243447 | 0.00993042 | 0.00496521 | − | 0.999988i | \(-0.498420\pi\) | ||||
0.00496521 | + | 0.999988i | \(0.498420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.8887 | + | 24.0559i | 0.564655 | + | 0.978011i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.985363 | + | 1.70670i | −0.0399947 | + | 0.0692728i | −0.885330 | − | 0.464964i | \(-0.846067\pi\) |
0.845335 | + | 0.534236i | \(0.179401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7302 | − | 35.9057i | 0.838652 | − | 1.45259i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.1837 | − | 26.2989i | −0.613262 | − | 1.06220i | −0.990687 | − | 0.136161i | \(-0.956524\pi\) |
0.377424 | − | 0.926040i | \(-0.376810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.1284 | −1.85706 | −0.928529 | − | 0.371259i | \(-0.878926\pi\) | ||||
−0.928529 | + | 0.371259i | \(0.878926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.4648 | − | 37.1781i | −0.862742 | − | 1.49431i | −0.869272 | − | 0.494335i | \(-0.835412\pi\) |
0.00652956 | − | 0.999979i | \(-0.497922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.32728 | + | 1.70956i | 0.333625 | + | 0.0684922i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.49957 | 0.179409 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.3019 | 1.76363 | 0.881816 | − | 0.471594i | \(-0.156321\pi\) | ||||
0.881816 | + | 0.471594i | \(0.156321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.5255 | + | 18.2307i | −0.417692 | + | 0.723464i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1325 | − | 15.8075i | 0.837300 | − | 0.626315i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1774 | − | 31.4841i | −0.717963 | − | 1.24355i | −0.961805 | − | 0.273734i | \(-0.911741\pi\) |
0.243842 | − | 0.969815i | \(-0.421592\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.17731 | −0.125301 | −0.0626504 | − | 0.998036i | \(-0.519955\pi\) | ||||
−0.0626504 | + | 0.998036i | \(0.519955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.5687 | − | 30.4299i | −0.690697 | − | 1.19632i | −0.971610 | − | 0.236589i | \(-0.923971\pi\) |
0.280913 | − | 0.959733i | \(-0.409363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.9270 | − | 44.9069i | 1.01772 | − | 1.76275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.58835 | − | 2.75110i | 0.0621569 | − | 0.107659i | −0.833272 | − | 0.552863i | \(-0.813535\pi\) |
0.895429 | + | 0.445204i | \(0.146869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.04997 | − | 1.81860i | −0.0410257 | − | 0.0710587i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.70542 | −0.105388 | −0.0526941 | − | 0.998611i | \(-0.516781\pi\) | ||||
−0.0526941 | + | 0.998611i | \(0.516781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8490 | + | 23.9871i | 0.538662 | + | 0.932990i | 0.998976 | + | 0.0452341i | \(0.0144034\pi\) |
−0.460314 | + | 0.887756i | \(0.652263\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.726062 | + | 0.817742i | −0.0281555 | + | 0.0317107i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.42663 | + | 14.5954i | −0.326280 | + | 0.565134i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9993 | −0.463228 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0997 | −1.04462 | −0.522309 | − | 0.852757i | \(-0.674929\pi\) | ||||
−0.522309 | + | 0.852757i | \(0.674929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.5828 | − | 40.8466i | 0.906360 | − | 1.56986i | 0.0872789 | − | 0.996184i | \(-0.472183\pi\) |
0.819081 | − | 0.573678i | \(-0.194484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4410 | + | 34.3958i | 0.439065 | + | 1.31999i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8742 | − | 22.2988i | −0.492619 | − | 0.853242i | 0.507345 | − | 0.861743i | \(-0.330627\pi\) |
−0.999964 | + | 0.00850171i | \(0.997294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2806 | −0.431008 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.02344 | − | 1.77264i | −0.0389898 | − | 0.0675324i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.3085 | − | 40.3715i | 0.886696 | − | 1.53580i | 0.0429396 | − | 0.999078i | \(-0.486328\pi\) |
0.843757 | − | 0.536726i | \(-0.180339\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.85174 | − | 3.20731i | 0.0702406 | − | 0.121660i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.53053 | + | 2.65096i | 0.0579731 | + | 0.100412i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.52122 | 0.132995 | 0.0664974 | − | 0.997787i | \(-0.478818\pi\) | ||||
0.0664974 | + | 0.997787i | \(0.478818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.48454 | − | 2.57130i | −0.0559906 | − | 0.0969785i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.9707 | − | 30.3763i | 1.01434 | − | 1.14242i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5337 | + | 23.4410i | −0.508267 | + | 0.880345i | 0.491687 | + | 0.870772i | \(0.336380\pi\) |
−0.999954 | + | 0.00957261i | \(0.996953\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.3503 | −1.32388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.4768 | 0.877982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.59672 | − | 4.49766i | 0.0968415 | − | 0.167734i | −0.813534 | − | 0.581517i | \(-0.802459\pi\) |
0.910376 | + | 0.413783i | \(0.135793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.6756 | − | 6.09231i | −1.10518 | − | 0.226889i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.06360 | − | 3.57426i | −0.0766403 | − | 0.132745i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9507 | −0.443228 | −0.221614 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221614 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.32723 | + | 5.76293i | 0.123062 | + | 0.213150i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.79754 | − | 6.57754i | 0.140265 | − | 0.242947i | −0.787331 | − | 0.616530i | \(-0.788538\pi\) |
0.927597 | + | 0.373584i | \(0.121871\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8274 | + | 37.8061i | −0.804022 | + | 1.39261i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.8275 | − | 43.0025i | −0.913294 | − | 1.58187i | −0.809380 | − | 0.587285i | \(-0.800197\pi\) |
−0.103913 | − | 0.994586i | \(-0.533136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3163 | 0.671960 | 0.335980 | − | 0.941869i | \(-0.390933\pi\) | ||||
0.335980 | + | 0.941869i | \(0.390933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.26686 | − | 12.5866i | −0.266237 | − | 0.461136i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.80680 | − | 1.39741i | −0.248715 | − | 0.0510604i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.2827 | + | 26.4704i | −0.557673 | + | 0.965918i | 0.440017 | + | 0.897989i | \(0.354972\pi\) |
−0.997690 | + | 0.0679284i | \(0.978361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.86762 | 0.213544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.82022 | 0.138848 | 0.0694241 | − | 0.997587i | \(-0.477884\pi\) | ||||
0.0694241 | + | 0.997587i | \(0.477884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.6217 | + | 33.9857i | −0.711285 | + | 1.23198i | 0.253090 | + | 0.967443i | \(0.418553\pi\) |
−0.964375 | + | 0.264539i | \(0.914780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.70110 | − | 8.67352i | 0.278798 | − | 0.314002i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.6969 | − | 27.1878i | −0.566781 | − | 0.981693i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4415 | 0.520774 | 0.260387 | − | 0.965504i | \(-0.416150\pi\) | ||||
0.260387 | + | 0.965504i | \(0.416150\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.63807 | + | 16.6936i | 0.346657 | + | 0.600428i | 0.985653 | − | 0.168782i | \(-0.0539834\pi\) |
−0.638996 | + | 0.769210i | \(0.720650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.32848 | − | 7.49714i | 0.155484 | − | 0.269305i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00994 | − | 1.74926i | 0.0361848 | − | 0.0626739i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.3813 | − | 66.4783i | −1.37339 | − | 2.37878i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.92659 | 0.318604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97274 | + | 3.41688i | 0.0703205 | + | 0.121799i | 0.899042 | − | 0.437863i | \(-0.144264\pi\) |
−0.828721 | + | 0.559662i | \(0.810931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.45947 | − | 13.4068i | −0.158560 | − | 0.476690i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.63234 | + | 6.29141i | −0.128988 | + | 0.223414i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.9932 | 1.23952 | 0.619761 | − | 0.784791i | \(-0.287230\pi\) | ||||
0.619761 | + | 0.784791i | \(0.287230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.88848 | 0.243697 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.1001 | + | 27.8863i | −0.568161 | + | 0.984084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.17314 | + | 8.07889i | −0.252820 | + | 0.284743i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.8931 | + | 20.5995i | 0.418139 | + | 0.724239i | 0.995752 | − | 0.0920722i | \(-0.0293490\pi\) |
−0.577613 | + | 0.816311i | \(0.696016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.9756 | 1.26327 | 0.631637 | − | 0.775264i | \(-0.282383\pi\) | ||||
0.631637 | + | 0.775264i | \(0.282383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.78694 | + | 8.29123i | 0.167679 | + | 0.290429i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.19551 | − | 3.80273i | 0.0768110 | − | 0.133041i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1929 | − | 19.3866i | 0.390633 | − | 0.676597i | −0.601900 | − | 0.798572i | \(-0.705589\pi\) |
0.992533 | + | 0.121975i | \(0.0389227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.23363 | + | 3.86876i | 0.0778595 | + | 0.134857i | 0.902326 | − | 0.431054i | \(-0.141858\pi\) |
−0.824467 | + | 0.565910i | \(0.808525\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1083 | 0.351499 | 0.175750 | − | 0.984435i | \(-0.443765\pi\) | ||||
0.175750 | + | 0.984435i | \(0.443765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.9421 | + | 48.3971i | 0.970469 | + | 1.68090i | 0.694143 | + | 0.719837i | \(0.255783\pi\) |
0.276325 | + | 0.961064i | \(0.410883\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.03003 | + | 1.72752i | 0.139632 | + | 0.0598549i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.04173 | − | 1.80433i | 0.0360505 | − | 0.0624413i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.81270 | −0.200677 | −0.100338 | − | 0.994953i | \(-0.531993\pi\) | ||||
−0.100338 | + | 0.994953i | \(0.531993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9662 | −0.412627 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.606722 | − | 1.05087i | 0.0208719 | − | 0.0361511i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −71.9905 | − | 14.7794i | −2.47362 | − | 0.507827i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6665 | − | 25.4032i | −0.502763 | − | 0.870811i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.12408 | −0.243924 | −0.121962 | − | 0.992535i | \(-0.538919\pi\) | ||||
−0.121962 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8602 | − | 20.5424i | −0.405135 | − | 0.701715i | 0.589202 | − | 0.807986i | \(-0.299442\pi\) |
−0.994337 | + | 0.106271i | \(0.966109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.10312 | + | 14.0350i | −0.276475 | + | 0.478869i | −0.970506 | − | 0.241076i | \(-0.922500\pi\) |
0.694031 | + | 0.719945i | \(0.255833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.9160 | + | 29.2993i | −0.575826 | + | 0.997361i | 0.420125 | + | 0.907466i | \(0.361986\pi\) |
−0.995951 | + | 0.0898943i | \(0.971347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.39867 | + | 2.42256i | 0.0475561 | + | 0.0823696i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.5623 | 1.51167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2148 | + | 22.8888i | 0.447768 | + | 0.775557i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.835066 | − | 2.51051i | −0.0282304 | − | 0.0848708i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.44312 | + | 5.96366i | −0.116266 | + | 0.201378i | −0.918285 | − | 0.395920i | \(-0.870426\pi\) |
0.802019 | + | 0.597298i | \(0.203759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.26521 | −0.244771 | −0.122386 | − | 0.992483i | \(-0.539054\pi\) | ||||
−0.122386 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.42372 | 0.216175 | 0.108088 | − | 0.994141i | \(-0.465527\pi\) | ||||
0.108088 | + | 0.994141i | \(0.465527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6147 | + | 39.1697i | −0.759326 | + | 1.31519i | 0.183869 | + | 0.982951i | \(0.441138\pi\) |
−0.943195 | + | 0.332240i | \(0.892196\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.5790 | − | 52.8488i | −0.589580 | − | 1.77249i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.27272 | − | 3.93646i | −0.0760536 | − | 0.131729i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4667 | 0.416717 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8645 | + | 30.9422i | 0.595815 | + | 1.03198i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.170040 | − | 0.294518i | 0.00566486 | − | 0.00981183i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.1158 | + | 22.7173i | −0.435984 | + | 0.755147i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8247 | − | 18.7489i | −0.359428 | − | 0.622547i | 0.628438 | − | 0.777860i | \(-0.283695\pi\) |
−0.987865 | + | 0.155313i | \(0.950361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.3615 | 0.674607 | 0.337304 | − | 0.941396i | \(-0.390485\pi\) | ||||
0.337304 | + | 0.941396i | \(0.390485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.3043 | + | 54.2206i | 1.03602 | + | 1.79444i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.44242 | + | 1.11731i | 0.179724 | + | 0.0368968i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.41193 | + | 11.1058i | −0.211510 | + | 0.366346i | −0.952187 | − | 0.305515i | \(-0.901171\pi\) |
0.740677 | + | 0.671861i | \(0.234505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.4740 | −1.52971 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.18340 | 0.236189 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3372 | + | 33.4930i | −0.634433 | + | 1.09887i | 0.352202 | + | 0.935924i | \(0.385433\pi\) |
−0.986635 | + | 0.162946i | \(0.947900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.342431 | − | 2.87295i | −0.0112227 | − | 0.0941570i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.95029 | + | 3.37801i | 0.0637814 | + | 0.110473i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.2833 | 1.41401 | 0.707003 | − | 0.707211i | \(-0.250047\pi\) | ||||
0.707003 | + | 0.707211i | \(0.250047\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.0275 | + | 50.2770i | 0.946268 | + | 1.63898i | 0.753192 | + | 0.657801i | \(0.228513\pi\) |
0.193077 | + | 0.981184i | \(0.438153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.97769 | − | 17.2819i | 0.324918 | − | 0.562775i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.58614 | − | 2.74727i | 0.0515425 | − | 0.0892743i | −0.839103 | − | 0.543973i | \(-0.816920\pi\) |
0.890646 | + | 0.454698i | \(0.150253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.74743 | + | 16.8830i | 0.316415 | + | 0.548047i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1066 | −0.942857 | −0.471428 | − | 0.881904i | \(-0.656261\pi\) | ||||
−0.471428 | + | 0.881904i | \(0.656261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.29652 | − | 5.70973i | −0.106673 | − | 0.184763i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8158 | − | 22.3179i | 0.639886 | − | 0.720684i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9714 | + | 38.0556i | −0.708756 | + | 1.22760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.10999 | 0.132305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5305 | −0.467271 | −0.233635 | − | 0.972324i | \(-0.575062\pi\) | ||||
−0.233635 | + | 0.972324i | \(0.575062\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0841 | − | 33.0547i | 0.612438 | − | 1.06077i | −0.378390 | − | 0.925646i | \(-0.623522\pi\) |
0.990828 | − | 0.135128i | \(-0.0431446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.09265 | + | 9.29764i | 0.0991459 | + | 0.298069i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.5255 | + | 25.1589i | 0.464713 | + | 0.804906i | 0.999189 | − | 0.0402779i | \(-0.0128243\pi\) |
−0.534476 | + | 0.845184i | \(0.679491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0082 | −0.639464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.659360 | − | 1.14204i | −0.0210303 | − | 0.0364256i | 0.855319 | − | 0.518102i | \(-0.173361\pi\) |
−0.876349 | + | 0.481677i | \(0.840028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.25848 | + | 9.10796i | −0.167549 | + | 0.290204i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.6905 | − | 37.5691i | 0.689718 | − | 1.19463i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2391 | − | 21.1987i | −0.388787 | − | 0.673398i | 0.603500 | − | 0.797363i | \(-0.293772\pi\) |
−0.992287 | + | 0.123965i | \(0.960439\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.16056 | 0.131899 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0846554 | − | 0.146627i | −0.00268106 | − | 0.00464374i | 0.864682 | − | 0.502320i | \(-0.167520\pi\) |
−0.867363 | + | 0.497676i | \(0.834187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2520.2.bi.s.1801.4 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.r.1801.4 | yes | 10 | ||
7.4 | even | 3 | inner | 2520.2.bi.s.361.4 | yes | 10 | |
21.11 | odd | 6 | 2520.2.bi.r.361.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.4 | ✓ | 10 | 21.11 | odd | 6 | ||
2520.2.bi.r.1801.4 | yes | 10 | 3.2 | odd | 2 | ||
2520.2.bi.s.361.4 | yes | 10 | 7.4 | even | 3 | inner | |
2520.2.bi.s.1801.4 | yes | 10 | 1.1 | even | 1 | trivial |