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.r.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 | \(0.221374\pi\) |
0.171022 | + | 0.985267i | \(0.445293\pi\) | |||||||
\(12\) | 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 | 0.901503 | − | 0.432772i | \(-0.142464\pi\) |
−0.825543 | + | 0.564339i | \(0.809131\pi\) | |||||||
\(18\) | 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 | −0.570758 | − | 0.821118i | \(-0.693351\pi\) |
0.996488 | + | 0.0837323i | \(0.0266841\pi\) | |||||||
\(24\) | 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 | \(-0.625178\pi\) | ||||
−0.383201 | + | 0.923665i | \(0.625178\pi\) | |||||||
\(30\) | 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 | \(-0.375373\pi\) | ||||
0.381601 | + | 0.924327i | \(0.375373\pi\) | |||||||
\(42\) | 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 | \(-0.537074\pi\) |
0.918262 | − | 0.395974i | \(-0.129593\pi\) | |||||||
\(48\) | 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 | 0.846779 | − | 0.531945i | \(-0.178539\pi\) |
−0.884067 | + | 0.467360i | \(0.845205\pi\) | |||||||
\(54\) | 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 | \(-0.984316\pi\) |
0.456739 | − | 0.889601i | \(-0.349017\pi\) | |||||||
\(60\) | 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 | \(-0.761169\pi\) | ||||
−0.731478 | + | 0.681865i | \(0.761169\pi\) | |||||||
\(72\) | 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 | \(-0.313944\pi\) | ||||
0.551793 | + | 0.833981i | \(0.313944\pi\) | |||||||
\(84\) | 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 | −0.938522 | − | 0.345220i | \(-0.887804\pi\) |
0.768230 | + | 0.640174i | \(0.221138\pi\) | |||||||
\(90\) | 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 | \(0.110037\pi\) |
−0.176970 | + | 0.984216i | \(0.556630\pi\) | |||||||
\(102\) | 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 | −0.795543 | − | 0.605897i | \(-0.792814\pi\) |
0.922494 | + | 0.386012i | \(0.126148\pi\) | |||||||
\(108\) | 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 | \(-0.419180\pi\) | ||||
0.251185 | + | 0.967939i | \(0.419180\pi\) | |||||||
\(114\) | 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 | −0.908242 | − | 0.418446i | \(-0.862575\pi\) |
0.816505 | + | 0.577338i | \(0.195908\pi\) | |||||||
\(132\) | 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 | 0.999784 | − | 0.0207966i | \(-0.00662023\pi\) |
−0.517902 | + | 0.855440i | \(0.673287\pi\) | |||||||
\(138\) | 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 | \(0.369643\pi\) |
−0.993501 | + | 0.113823i | \(0.963690\pi\) | |||||||
\(150\) | 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 | \(-0.525687\pi\) | ||||
−0.0806114 | + | 0.996746i | \(0.525687\pi\) | |||||||
\(168\) | 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 | −0.807946 | − | 0.589257i | \(-0.799421\pi\) |
0.914284 | + | 0.405073i | \(0.132754\pi\) | |||||||
\(174\) | 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 | 0.533338 | − | 0.845902i | \(-0.320937\pi\) |
−0.999242 | + | 0.0389331i | \(0.987604\pi\) | |||||||
\(180\) | 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 | −0.960292 | − | 0.278997i | \(-0.909998\pi\) |
0.721764 | + | 0.692139i | \(0.243331\pi\) | |||||||
\(192\) | 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 | \(-0.377762\pi\) | ||||
0.374651 | + | 0.927166i | \(0.377762\pi\) | |||||||
\(198\) | 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 | 0.970145 | − | 0.242526i | \(-0.0779759\pi\) |
−0.695106 | + | 0.718907i | \(0.744643\pi\) | |||||||
\(228\) | 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 | −0.564894 | − | 0.825164i | \(-0.691083\pi\) |
0.997060 | + | 0.0766306i | \(0.0244162\pi\) | |||||||
\(234\) | 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 | \(-0.234391\pi\) | ||||
0.740916 | + | 0.671597i | \(0.234391\pi\) | |||||||
\(240\) | 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 | \(-0.384728\pi\) | ||||
0.354274 | + | 0.935142i | \(0.384728\pi\) | |||||||
\(252\) | 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 | \(0.353952\pi\) |
−0.997903 | + | 0.0647296i | \(0.979382\pi\) | |||||||
\(258\) | 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 | \(-0.789550\pi\) |
−0.137117 | − | 0.990555i | \(-0.543784\pi\) | |||||||
\(264\) | 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 | \(0.119589\pi\) |
−0.147361 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(270\) | 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 | \(-0.463975\pi\) | ||||
0.112933 | + | 0.993603i | \(0.463975\pi\) | |||||||
\(282\) | 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 | \(-0.823495\pi\) | ||||
−0.850161 | + | 0.526523i | \(0.823495\pi\) | |||||||
\(294\) | 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 | 0.734789 | − | 0.678295i | \(-0.237281\pi\) |
−0.954816 | + | 0.297199i | \(0.903948\pi\) | |||||||
\(312\) | 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 | −0.926650 | − | 0.375924i | \(-0.877325\pi\) |
0.788885 | + | 0.614541i | \(0.210659\pi\) | |||||||
\(318\) | 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 | 0.952177 | − | 0.305547i | \(-0.0988393\pi\) |
−0.740700 | + | 0.671836i | \(0.765506\pi\) | |||||||
\(348\) | 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 | 0.960784 | − | 0.277297i | \(-0.0894387\pi\) |
−0.720539 | + | 0.693415i | \(0.756105\pi\) | |||||||
\(354\) | 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 | \(-0.614361\pi\) |
0.986529 | − | 0.163584i | \(-0.0523053\pi\) | |||||||
\(360\) | 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 | −0.626428 | − | 0.779479i | \(-0.715484\pi\) |
0.988263 | + | 0.152763i | \(0.0488171\pi\) | |||||||
\(384\) | 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 | \(-0.956625\pi\) |
0.377718 | − | 0.925921i | \(-0.376709\pi\) | |||||||
\(390\) | 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 | \(0.569063\pi\) |
−0.738087 | + | 0.674706i | \(0.764270\pi\) | |||||||
\(402\) | 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 | \(-0.585727\pi\) | ||||
−0.266075 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(420\) | 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 | \(0.0970846\pi\) |
−0.216862 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(432\) | 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 | \(-0.625113\pi\) |
0.991491 | − | 0.130173i | \(-0.0415533\pi\) | |||||||
\(444\) | 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 | \(-0.397970\pi\) | ||||
0.315077 | + | 0.949066i | \(0.397970\pi\) | |||||||
\(450\) | 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 | \(-0.553221\pi\) | ||||
−0.166419 | + | 0.986055i | \(0.553221\pi\) | |||||||
\(462\) | 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 | \(-0.641117\pi\) |
0.996780 | − | 0.0801813i | \(-0.0255499\pi\) | |||||||
\(468\) | 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 | \(0.0678904\pi\) |
−0.305358 | + | 0.952237i | \(0.598776\pi\) | |||||||
\(480\) | 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 | \(-0.272983\pi\) | ||||
0.654254 | + | 0.756275i | \(0.272983\pi\) | |||||||
\(492\) | 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 | \(-0.700768\pi\) | ||||
−0.589737 | + | 0.807596i | \(0.700768\pi\) | |||||||
\(504\) | 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 | −0.895108 | − | 0.445850i | \(-0.852901\pi\) |
0.833671 | + | 0.552261i | \(0.186235\pi\) | |||||||
\(510\) | 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 | 0.870737 | − | 0.491749i | \(-0.163642\pi\) |
−0.861235 | + | 0.508206i | \(0.830309\pi\) | |||||||
\(522\) | 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 | 0.989144 | − | 0.146949i | \(-0.0469454\pi\) |
−0.621834 | + | 0.783149i | \(0.713612\pi\) | |||||||
\(558\) | 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 | \(-0.988302\pi\) |
0.467842 | − | 0.883812i | \(-0.345031\pi\) | |||||||
\(564\) | 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 | −0.713729 | − | 0.700422i | \(-0.752995\pi\) |
0.963448 | + | 0.267897i | \(0.0863287\pi\) | |||||||
\(570\) | 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 | \(-0.524769\pi\) | ||||
−0.0777355 | + | 0.996974i | \(0.524769\pi\) | |||||||
\(588\) | 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 | \(-0.566788\pi\) |
0.951175 | − | 0.308654i | \(-0.0998784\pi\) | |||||||
\(594\) | 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 | \(0.155185\pi\) |
−0.0360636 | + | 0.999349i | \(0.511482\pi\) | |||||||
\(600\) | 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 | \(-0.121074\pi\) | ||||
0.928529 | + | 0.371259i | \(0.121074\pi\) | |||||||
\(618\) | 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 | \(0.0882588\pi\) |
−0.243842 | + | 0.969815i | \(0.578408\pi\) | |||||||
\(642\) | 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 | \(0.0760294\pi\) |
−0.280913 | + | 0.959733i | \(0.590637\pi\) | |||||||
\(648\) | 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 | −0.895429 | − | 0.445204i | \(-0.853131\pi\) |
0.833272 | + | 0.552863i | \(0.186465\pi\) | |||||||
\(654\) | 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 | \(-0.483219\pi\) | ||||
0.0526941 | + | 0.998611i | \(0.483219\pi\) | |||||||
\(660\) | 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 | \(0.527817\pi\) |
−0.819081 | + | 0.573678i | \(0.805516\pi\) | |||||||
\(678\) | 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 | 0.999964 | − | 0.00850171i | \(-0.00270621\pi\) |
−0.507345 | + | 0.861743i | \(0.669373\pi\) | |||||||
\(684\) | 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 | \(-0.521182\pi\) | ||||
−0.0664974 | + | 0.997787i | \(0.521182\pi\) | |||||||
\(702\) | 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 | −0.910376 | − | 0.413783i | \(-0.864207\pi\) |
0.813534 | + | 0.581517i | \(0.197541\pi\) | |||||||
\(720\) | 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 | \(-0.609067\pi\) | ||||
−0.335980 | + | 0.941869i | \(0.609067\pi\) | |||||||
\(744\) | 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 | \(-0.581447\pi\) |
0.964375 | − | 0.264539i | \(-0.0852196\pi\) | |||||||
\(762\) | 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 | 0.638996 | − | 0.769210i | \(-0.279350\pi\) |
−0.985653 | + | 0.168782i | \(0.946017\pi\) | |||||||
\(774\) | 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 | \(-0.712770\pi\) | ||||
−0.619761 | + | 0.784791i | \(0.712770\pi\) | |||||||
\(798\) | 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 | 0.577613 | − | 0.816311i | \(-0.303984\pi\) |
−0.995752 | + | 0.0920722i | \(0.970651\pi\) | |||||||
\(810\) | 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 | −0.992533 | − | 0.121975i | \(-0.961077\pi\) |
0.601900 | + | 0.798572i | \(0.294411\pi\) | |||||||
\(822\) | 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 | \(-0.556235\pi\) | ||||
−0.175750 | + | 0.984435i | \(0.556235\pi\) | |||||||
\(828\) | 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 | \(-0.468007\pi\) | ||||
0.100338 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(840\) | 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 | 0.994337 | − | 0.106271i | \(-0.0338911\pi\) |
−0.589202 | + | 0.807986i | \(0.700558\pi\) | |||||||
\(858\) | 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 | \(-0.638014\pi\) |
0.995951 | − | 0.0898943i | \(-0.0286529\pi\) | |||||||
\(864\) | 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 | \(-0.460946\pi\) | ||||
0.122386 | + | 0.992483i | \(0.460946\pi\) | |||||||
\(882\) | 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 | \(-0.558862\pi\) |
0.943195 | − | 0.332240i | \(-0.107804\pi\) | |||||||
\(888\) | 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 | \(-0.609515\pi\) | ||||
−0.337304 | + | 0.941396i | \(0.609515\pi\) | |||||||
\(912\) | 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 | \(-0.614567\pi\) |
0.986635 | − | 0.162946i | \(-0.0520998\pi\) | |||||||
\(930\) | 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 | \(-0.771487\pi\) |
−0.193077 | − | 0.981184i | \(-0.561847\pi\) | |||||||
\(942\) | 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 | −0.890646 | − | 0.454698i | \(-0.849747\pi\) |
0.839103 | + | 0.543973i | \(0.183080\pi\) | |||||||
\(948\) | 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 | \(-0.343739\pi\) | ||||
0.471428 | + | 0.881904i | \(0.343739\pi\) | |||||||
\(954\) | 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 | \(0.376478\pi\) |
−0.990828 | + | 0.135128i | \(0.956855\pi\) | |||||||
\(972\) | 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 | 0.534476 | − | 0.845184i | \(-0.320509\pi\) |
−0.999189 | + | 0.0402779i | \(0.987176\pi\) | |||||||
\(978\) | 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 | 0.876349 | − | 0.481677i | \(-0.159972\pi\) |
−0.855319 | + | 0.518102i | \(0.826639\pi\) | |||||||
\(984\) | 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.r.1801.4 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.s.1801.4 | yes | 10 | ||
7.4 | even | 3 | inner | 2520.2.bi.r.361.4 | ✓ | 10 | |
21.11 | odd | 6 | 2520.2.bi.s.361.4 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.4 | ✓ | 10 | 7.4 | even | 3 | inner | |
2520.2.bi.r.1801.4 | yes | 10 | 1.1 | even | 1 | trivial | |
2520.2.bi.s.361.4 | yes | 10 | 21.11 | odd | 6 | ||
2520.2.bi.s.1801.4 | yes | 10 | 3.2 | odd | 2 |