Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Root | \(3.78139 - 0.0336790i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.107 |
Dual form | 225.4.f.c.143.6 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.74771 | − | 3.74771i | 1.32502 | − | 1.32502i | 0.415360 | − | 0.909657i | \(-0.363656\pi\) |
0.909657 | − | 0.415360i | \(-0.136344\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 20.0907i | − | 2.51134i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80948 | − | 1.80948i | −0.0977029 | − | 0.0977029i | 0.656566 | − | 0.754269i | \(-0.272008\pi\) |
−0.754269 | + | 0.656566i | \(0.772008\pi\) | |||||||
\(8\) | −45.3126 | − | 45.3126i | −2.00255 | − | 2.00255i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 46.0907i | − | 1.26335i | −0.775232 | − | 0.631676i | \(-0.782367\pi\) | ||
0.775232 | − | 0.631676i | \(-0.217633\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.6099 | + | 18.6099i | −0.397035 | + | 0.397035i | −0.877186 | − | 0.480151i | \(-0.840582\pi\) |
0.480151 | + | 0.877186i | \(0.340582\pi\) | |||||||
\(14\) | −13.5628 | −0.258916 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −178.911 | −2.79549 | ||||||||
\(17\) | −14.5793 | + | 14.5793i | −0.208000 | + | 0.208000i | −0.803417 | − | 0.595417i | \(-0.796987\pi\) |
0.595417 | + | 0.803417i | \(0.296987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 74.4577i | − | 0.899041i | −0.893270 | − | 0.449520i | \(-0.851595\pi\) | ||
0.893270 | − | 0.449520i | \(-0.148405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −172.735 | − | 172.735i | −1.67396 | − | 1.67396i | ||||
\(23\) | 59.6003 | + | 59.6003i | 0.540327 | + | 0.540327i | 0.923625 | − | 0.383298i | \(-0.125212\pi\) |
−0.383298 | + | 0.923625i | \(0.625212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 139.489i | 1.05216i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −36.3538 | + | 36.3538i | −0.245365 | + | 0.245365i | ||||
\(29\) | 202.168 | 1.29454 | 0.647271 | − | 0.762260i | \(-0.275910\pi\) | ||||
0.647271 | + | 0.762260i | \(0.275910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −49.5423 | −0.287034 | −0.143517 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143517 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(32\) | −308.008 | + | 308.008i | −1.70152 | + | 1.70152i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 109.278i | 0.551208i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 45.0594 | + | 45.0594i | 0.200209 | + | 0.200209i | 0.800089 | − | 0.599881i | \(-0.204785\pi\) |
−0.599881 | + | 0.800089i | \(0.704785\pi\) | |||||||
\(38\) | −279.046 | − | 279.046i | −1.19124 | − | 1.19124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 306.253i | 1.16655i | 0.812274 | + | 0.583276i | \(0.198229\pi\) | ||||
−0.812274 | + | 0.583276i | \(0.801771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 230.784 | − | 230.784i | 0.818472 | − | 0.818472i | −0.167415 | − | 0.985887i | \(-0.553542\pi\) |
0.985887 | + | 0.167415i | \(0.0535420\pi\) | |||||||
\(44\) | −925.996 | −3.17271 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 446.730 | 1.43189 | ||||||||
\(47\) | 176.943 | − | 176.943i | 0.549143 | − | 0.549143i | −0.377050 | − | 0.926193i | \(-0.623062\pi\) |
0.926193 | + | 0.377050i | \(0.123062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 336.452i | − | 0.980908i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 373.886 | + | 373.886i | 0.997090 | + | 0.997090i | ||||
\(53\) | 85.1290 | + | 85.1290i | 0.220630 | + | 0.220630i | 0.808764 | − | 0.588134i | \(-0.200137\pi\) |
−0.588134 | + | 0.808764i | \(0.700137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 163.985i | 0.391310i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 757.669 | − | 757.669i | 1.71529 | − | 1.71529i | ||||
\(59\) | 330.873 | 0.730103 | 0.365051 | − | 0.930987i | \(-0.381051\pi\) | ||||
0.365051 | + | 0.930987i | \(0.381051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 678.639 | 1.42444 | 0.712220 | − | 0.701956i | \(-0.247690\pi\) | ||||
0.712220 | + | 0.701956i | \(0.247690\pi\) | |||||||
\(62\) | −185.670 | + | 185.670i | −0.380325 | + | 0.380325i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 877.361i | 1.71360i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −756.373 | − | 756.373i | −1.37919 | − | 1.37919i | −0.845990 | − | 0.533199i | \(-0.820990\pi\) |
−0.533199 | − | 0.845990i | \(-0.679010\pi\) | |||||||
\(68\) | 292.909 | + | 292.909i | 0.522360 | + | 0.522360i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 100.264i | 0.167594i | 0.996483 | + | 0.0837972i | \(0.0267048\pi\) | ||||
−0.996483 | + | 0.0837972i | \(0.973295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −586.919 | + | 586.919i | −0.941010 | + | 0.941010i | −0.998354 | − | 0.0573449i | \(-0.981737\pi\) |
0.0573449 | + | 0.998354i | \(0.481737\pi\) | |||||||
\(74\) | 337.739 | 0.530560 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1495.91 | −2.25780 | ||||||||
\(77\) | −83.4004 | + | 83.4004i | −0.123433 | + | 0.123433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 286.986i | 0.408714i | 0.978896 | + | 0.204357i | \(0.0655103\pi\) | ||||
−0.978896 | + | 0.204357i | \(0.934490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1147.75 | + | 1147.75i | 1.54570 | + | 1.54570i | ||||
\(83\) | 947.796 | + | 947.796i | 1.25342 | + | 1.25342i | 0.954175 | + | 0.299248i | \(0.0967359\pi\) |
0.299248 | + | 0.954175i | \(0.403264\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1729.83i | − | 2.16898i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2088.49 | + | 2088.49i | −2.52993 | + | 2.52993i | ||||
\(89\) | 688.442 | 0.819941 | 0.409970 | − | 0.912099i | \(-0.365539\pi\) | ||||
0.409970 | + | 0.912099i | \(0.365539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 67.3485 | 0.0775829 | ||||||||
\(92\) | 1197.41 | − | 1197.41i | 1.35695 | − | 1.35695i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1326.26i | − | 1.45525i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −920.676 | − | 920.676i | −0.963716 | − | 0.963716i | 0.0356483 | − | 0.999364i | \(-0.488650\pi\) |
−0.999364 | + | 0.0356483i | \(0.988650\pi\) | |||||||
\(98\) | −1260.92 | − | 1260.92i | −1.29972 | − | 1.29972i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1018.42i | 1.00333i | 0.865061 | + | 0.501667i | \(0.167280\pi\) | ||||
−0.865061 | + | 0.501667i | \(0.832720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 381.856 | − | 381.856i | 0.365295 | − | 0.365295i | −0.500463 | − | 0.865758i | \(-0.666837\pi\) |
0.865758 | + | 0.500463i | \(0.166837\pi\) | |||||||
\(104\) | 1686.52 | 1.59017 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 638.078 | 0.584676 | ||||||||
\(107\) | −11.6954 | + | 11.6954i | −0.0105667 | + | 0.0105667i | −0.712370 | − | 0.701804i | \(-0.752378\pi\) |
0.701804 | + | 0.712370i | \(0.252378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1346.99i | − | 1.18366i | −0.806064 | − | 0.591828i | \(-0.798406\pi\) | ||
0.806064 | − | 0.591828i | \(-0.201594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 323.737 | + | 323.737i | 0.273127 | + | 0.273127i | ||||
\(113\) | −677.607 | − | 677.607i | −0.564105 | − | 0.564105i | 0.366366 | − | 0.930471i | \(-0.380602\pi\) |
−0.930471 | + | 0.366366i | \(0.880602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4061.71i | − | 3.25104i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1240.02 | − | 1240.02i | 0.967398 | − | 0.967398i | ||||
\(119\) | 52.7621 | 0.0406445 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −793.355 | −0.596059 | ||||||||
\(122\) | 2543.35 | − | 2543.35i | 1.88741 | − | 1.88741i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 995.340i | 0.720840i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1220.98 | + | 1220.98i | 0.853107 | + | 0.853107i | 0.990515 | − | 0.137408i | \(-0.0438771\pi\) |
−0.137408 | + | 0.990515i | \(0.543877\pi\) | |||||||
\(128\) | 824.034 | + | 824.034i | 0.569023 | + | 0.569023i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 215.023i | 0.143409i | 0.997426 | + | 0.0717046i | \(0.0228439\pi\) | ||||
−0.997426 | + | 0.0717046i | \(0.977156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −134.730 | + | 134.730i | −0.0878389 | + | 0.0878389i | ||||
\(134\) | −5669.34 | −3.65490 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1321.25 | 0.833063 | ||||||||
\(137\) | −877.965 | + | 877.965i | −0.547516 | + | 0.547516i | −0.925721 | − | 0.378206i | \(-0.876541\pi\) |
0.378206 | + | 0.925721i | \(0.376541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2489.62i | 1.51918i | 0.650400 | + | 0.759592i | \(0.274601\pi\) | ||||
−0.650400 | + | 0.759592i | \(0.725399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 375.762 | + | 375.762i | 0.222065 | + | 0.222065i | ||||
\(143\) | 857.743 | + | 857.743i | 0.501595 | + | 0.501595i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4399.21i | 2.49371i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 905.276 | − | 905.276i | 0.502792 | − | 0.502792i | ||||
\(149\) | 1497.94 | 0.823596 | 0.411798 | − | 0.911275i | \(-0.364901\pi\) | ||||
0.411798 | + | 0.911275i | \(0.364901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1614.69 | −0.870209 | −0.435104 | − | 0.900380i | \(-0.643289\pi\) | ||||
−0.435104 | + | 0.900380i | \(0.643289\pi\) | |||||||
\(152\) | −3373.87 | + | 3373.87i | −1.80038 | + | 1.80038i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 625.121i | 0.327102i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 456.938 | + | 456.938i | 0.232278 | + | 0.232278i | 0.813643 | − | 0.581365i | \(-0.197481\pi\) |
−0.581365 | + | 0.813643i | \(0.697481\pi\) | |||||||
\(158\) | 1075.54 | + | 1075.54i | 0.541553 | + | 0.541553i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 215.691i | − | 0.105583i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1434.13 | + | 1434.13i | −0.689140 | + | 0.689140i | −0.962042 | − | 0.272902i | \(-0.912017\pi\) |
0.272902 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(164\) | 6152.83 | 2.92961 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7104.14 | 3.32162 | ||||||||
\(167\) | −1129.18 | + | 1129.18i | −0.523226 | + | 0.523226i | −0.918544 | − | 0.395318i | \(-0.870634\pi\) |
0.395318 | + | 0.918544i | \(0.370634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1504.34i | 0.684726i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4636.62 | − | 4636.62i | −2.05546 | − | 2.05546i | ||||
\(173\) | 1656.73 | + | 1656.73i | 0.728084 | + | 0.728084i | 0.970238 | − | 0.242154i | \(-0.0778538\pi\) |
−0.242154 | + | 0.970238i | \(0.577854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8246.15i | 3.53169i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2580.08 | − | 2580.08i | 1.08644 | − | 1.08644i | ||||
\(179\) | −1449.32 | −0.605180 | −0.302590 | − | 0.953121i | \(-0.597851\pi\) | ||||
−0.302590 | + | 0.953121i | \(0.597851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1120.24 | −0.460037 | −0.230019 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230019 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(182\) | 252.403 | − | 252.403i | 0.102799 | − | 0.102799i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5401.29i | − | 2.16407i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 671.972 | + | 671.972i | 0.262778 | + | 0.262778i | ||||
\(188\) | −3554.90 | − | 3554.90i | −1.37908 | − | 1.37908i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3827.59i | − | 1.45002i | −0.688737 | − | 0.725012i | \(-0.741834\pi\) | ||
0.688737 | − | 0.725012i | \(-0.258166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1792.85 | + | 1792.85i | −0.668665 | + | 0.668665i | −0.957407 | − | 0.288742i | \(-0.906763\pi\) |
0.288742 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(194\) | −6900.86 | −2.55388 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6759.55 | −2.46339 | ||||||||
\(197\) | −2222.09 | + | 2222.09i | −0.803640 | + | 0.803640i | −0.983663 | − | 0.180022i | \(-0.942383\pi\) |
0.180022 | + | 0.983663i | \(0.442383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1421.45i | 0.506352i | 0.967420 | + | 0.253176i | \(0.0814752\pi\) | ||||
−0.967420 | + | 0.253176i | \(0.918525\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3816.75 | + | 3816.75i | 1.32943 | + | 1.32943i | ||||
\(203\) | −365.820 | − | 365.820i | −0.126481 | − | 0.126481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2862.17i | − | 0.968043i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3329.52 | − | 3329.52i | 1.10991 | − | 1.10991i | ||||
\(209\) | −3431.81 | −1.13580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1133.67 | 0.369883 | 0.184942 | − | 0.982749i | \(-0.440790\pi\) | ||||
0.184942 | + | 0.982749i | \(0.440790\pi\) | |||||||
\(212\) | 1710.30 | − | 1710.30i | 0.554076 | − | 0.554076i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 87.6623i | 0.0280022i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 89.6459 | + | 89.6459i | 0.0280441 | + | 0.0280441i | ||||
\(218\) | −5048.15 | − | 5048.15i | −1.56837 | − | 1.56837i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 542.639i | − | 0.165167i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −666.458 | + | 666.458i | −0.200131 | + | 0.200131i | −0.800056 | − | 0.599925i | \(-0.795197\pi\) |
0.599925 | + | 0.800056i | \(0.295197\pi\) | |||||||
\(224\) | 1114.67 | 0.332487 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5078.95 | −1.49490 | ||||||||
\(227\) | 2292.99 | − | 2292.99i | 0.670446 | − | 0.670446i | −0.287373 | − | 0.957819i | \(-0.592782\pi\) |
0.957819 | + | 0.287373i | \(0.0927819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2535.40i | 0.731634i | 0.930687 | + | 0.365817i | \(0.119210\pi\) | ||||
−0.930687 | + | 0.365817i | \(0.880790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9160.77 | − | 9160.77i | −2.59239 | − | 2.59239i | ||||
\(233\) | −1699.70 | − | 1699.70i | −0.477902 | − | 0.477902i | 0.426558 | − | 0.904460i | \(-0.359726\pi\) |
−0.904460 | + | 0.426558i | \(0.859726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 6647.49i | − | 1.83354i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 197.737 | − | 197.737i | 0.0538546 | − | 0.0538546i | ||||
\(239\) | 3948.41 | 1.06863 | 0.534313 | − | 0.845287i | \(-0.320570\pi\) | ||||
0.534313 | + | 0.845287i | \(0.320570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2447.20 | −0.654101 | −0.327050 | − | 0.945007i | \(-0.606055\pi\) | ||||
−0.327050 | + | 0.945007i | \(0.606055\pi\) | |||||||
\(242\) | −2973.27 | + | 2973.27i | −0.789788 | + | 0.789788i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 13634.3i | − | 3.57725i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1385.65 | + | 1385.65i | 0.356951 | + | 0.356951i | ||||
\(248\) | 2244.89 | + | 2244.89i | 0.574801 | + | 0.574801i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4755.75i | 1.19594i | 0.801519 | + | 0.597969i | \(0.204025\pi\) | ||||
−0.801519 | + | 0.597969i | \(0.795975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2747.02 | − | 2747.02i | 0.682624 | − | 0.682624i | ||||
\(254\) | 9151.78 | 2.26076 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −842.400 | −0.205664 | ||||||||
\(257\) | 1127.34 | − | 1127.34i | 0.273624 | − | 0.273624i | −0.556933 | − | 0.830557i | \(-0.688022\pi\) |
0.830557 | + | 0.556933i | \(0.188022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 163.068i | − | 0.0391219i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 805.843 | + | 805.843i | 0.190020 | + | 0.190020i | ||||
\(263\) | 358.621 | + | 358.621i | 0.0840817 | + | 0.0840817i | 0.747897 | − | 0.663815i | \(-0.231064\pi\) |
−0.663815 | + | 0.747897i | \(0.731064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1009.86i | 0.232776i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15196.1 | + | 15196.1i | −3.46361 | + | 3.46361i | ||||
\(269\) | −3824.41 | −0.866834 | −0.433417 | − | 0.901193i | \(-0.642692\pi\) | ||||
−0.433417 | + | 0.901193i | \(0.642692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 535.546 | 0.120045 | 0.0600223 | − | 0.998197i | \(-0.480883\pi\) | ||||
0.0600223 | + | 0.998197i | \(0.480883\pi\) | |||||||
\(272\) | 2608.41 | − | 2608.41i | 0.581463 | − | 0.581463i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6580.72i | 1.45093i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1108.08 | − | 1108.08i | −0.240354 | − | 0.240354i | 0.576643 | − | 0.816996i | \(-0.304362\pi\) |
−0.816996 | + | 0.576643i | \(0.804362\pi\) | |||||||
\(278\) | 9330.37 | + | 9330.37i | 2.01294 | + | 2.01294i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3439.91i | 0.730277i | 0.930953 | + | 0.365139i | \(0.118978\pi\) | ||||
−0.930953 | + | 0.365139i | \(0.881022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2726.08 | + | 2726.08i | −0.572610 | + | 0.572610i | −0.932857 | − | 0.360247i | \(-0.882693\pi\) |
0.360247 | + | 0.932857i | \(0.382693\pi\) | |||||||
\(284\) | 2014.38 | 0.420886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6429.15 | 1.32924 | ||||||||
\(287\) | 554.159 | − | 554.159i | 0.113975 | − | 0.113975i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4487.89i | 0.913472i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11791.6 | + | 11791.6i | 2.36320 | + | 2.36320i | ||||
\(293\) | −4347.55 | − | 4347.55i | −0.866849 | − | 0.866849i | 0.125273 | − | 0.992122i | \(-0.460019\pi\) |
−0.992122 | + | 0.125273i | \(0.960019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4083.51i | − | 0.801856i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5613.84 | − | 5613.84i | 1.09128 | − | 1.09128i | ||||
\(299\) | −2218.31 | −0.429058 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −835.200 | −0.159934 | ||||||||
\(302\) | −6051.39 | + | 6051.39i | −1.15304 | + | 1.15304i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13321.3i | 2.51326i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3137.18 | − | 3137.18i | −0.583220 | − | 0.583220i | 0.352567 | − | 0.935787i | \(-0.385309\pi\) |
−0.935787 | + | 0.352567i | \(0.885309\pi\) | |||||||
\(308\) | 1675.57 | + | 1675.57i | 0.309983 | + | 0.309983i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8268.00i | − | 1.50751i | −0.657157 | − | 0.753754i | \(-0.728241\pi\) | ||
0.657157 | − | 0.753754i | \(-0.271759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4673.46 | − | 4673.46i | 0.843959 | − | 0.843959i | −0.145412 | − | 0.989371i | \(-0.546451\pi\) |
0.989371 | + | 0.145412i | \(0.0464507\pi\) | |||||||
\(314\) | 3424.95 | 0.615544 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5765.75 | 1.02642 | ||||||||
\(317\) | −3271.78 | + | 3271.78i | −0.579690 | + | 0.579690i | −0.934818 | − | 0.355128i | \(-0.884437\pi\) |
0.355128 | + | 0.934818i | \(0.384437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9318.09i | − | 1.63546i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −808.350 | − | 808.350i | −0.139899 | − | 0.139899i | ||||
\(323\) | 1085.54 | + | 1085.54i | 0.187001 | + | 0.187001i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10749.4i | 1.82624i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13877.1 | − | 13877.1i | 2.33608 | − | 2.33608i | ||||
\(329\) | −640.349 | −0.107306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9665.06 | 1.60495 | 0.802477 | − | 0.596684i | \(-0.203515\pi\) | ||||
0.802477 | + | 0.596684i | \(0.203515\pi\) | |||||||
\(332\) | 19041.9 | − | 19041.9i | 3.14777 | − | 3.14777i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8463.70i | 1.38657i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1911.95 | − | 1911.95i | −0.309053 | − | 0.309053i | 0.535489 | − | 0.844542i | \(-0.320127\pi\) |
−0.844542 | + | 0.535489i | \(0.820127\pi\) | |||||||
\(338\) | 5637.85 | + | 5637.85i | 0.907274 | + | 0.907274i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2283.44i | 0.362625i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1229.46 | + | 1229.46i | −0.193540 | + | 0.193540i | ||||
\(344\) | −20914.9 | −3.27806 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12417.9 | 1.92945 | ||||||||
\(347\) | 7023.71 | − | 7023.71i | 1.08661 | − | 1.08661i | 0.0907318 | − | 0.995875i | \(-0.471079\pi\) |
0.995875 | − | 0.0907318i | \(-0.0289206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9259.70i | − | 1.42023i | −0.704085 | − | 0.710115i | \(-0.748643\pi\) | ||
0.704085 | − | 0.710115i | \(-0.251357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14196.3 | + | 14196.3i | 2.14962 | + | 2.14962i | ||||
\(353\) | 4338.33 | + | 4338.33i | 0.654125 | + | 0.654125i | 0.953984 | − | 0.299859i | \(-0.0969396\pi\) |
−0.299859 | + | 0.953984i | \(0.596940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13831.3i | − | 2.05915i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5431.64 | + | 5431.64i | −0.801874 | + | 0.801874i | ||||
\(359\) | 5949.44 | 0.874650 | 0.437325 | − | 0.899304i | \(-0.355926\pi\) | ||||
0.437325 | + | 0.899304i | \(0.355926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1315.05 | 0.191726 | ||||||||
\(362\) | −4198.34 | + | 4198.34i | −0.609557 | + | 0.609557i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 1353.08i | − | 0.194837i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9153.79 | + | 9153.79i | 1.30197 | + | 1.30197i | 0.927061 | + | 0.374912i | \(0.122327\pi\) |
0.374912 | + | 0.927061i | \(0.377673\pi\) | |||||||
\(368\) | −10663.2 | − | 10663.2i | −1.51048 | − | 1.51048i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 308.079i | − | 0.0431123i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6473.68 | − | 6473.68i | 0.898644 | − | 0.898644i | −0.0966723 | − | 0.995316i | \(-0.530820\pi\) |
0.995316 | + | 0.0966723i | \(0.0308199\pi\) | |||||||
\(374\) | 5036.72 | 0.696370 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16035.4 | −2.19937 | ||||||||
\(377\) | −3762.33 | + | 3762.33i | −0.513979 | + | 0.513979i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 245.031i | 0.0332094i | 0.999862 | + | 0.0166047i | \(0.00528569\pi\) | ||||
−0.999862 | + | 0.0166047i | \(0.994714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14344.7 | − | 14344.7i | −1.92131 | − | 1.92131i | ||||
\(383\) | −4476.48 | − | 4476.48i | −0.597225 | − | 0.597225i | 0.342348 | − | 0.939573i | \(-0.388778\pi\) |
−0.939573 | + | 0.342348i | \(0.888778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13438.2i | 1.77199i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18497.0 | + | 18497.0i | −2.42022 | + | 2.42022i | ||||
\(389\) | −4429.26 | −0.577307 | −0.288654 | − | 0.957434i | \(-0.593208\pi\) | ||||
−0.288654 | + | 0.957434i | \(0.593208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1737.87 | −0.224777 | ||||||||
\(392\) | −15245.5 | + | 15245.5i | −1.96432 | + | 1.96432i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16655.5i | 2.12967i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4786.16 | − | 4786.16i | −0.605065 | − | 0.605065i | 0.336588 | − | 0.941652i | \(-0.390727\pi\) |
−0.941652 | + | 0.336588i | \(0.890727\pi\) | |||||||
\(398\) | 5327.19 | + | 5327.19i | 0.670925 | + | 0.670925i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4521.85i | − | 0.563119i | −0.959544 | − | 0.281559i | \(-0.909148\pi\) | ||
0.959544 | − | 0.281559i | \(-0.0908516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 921.977 | − | 921.977i | 0.113963 | − | 0.113963i | ||||
\(404\) | 20460.8 | 2.51971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2741.98 | −0.335178 | ||||||||
\(407\) | 2076.82 | − | 2076.82i | 0.252934 | − | 0.252934i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10162.9i | − | 1.22866i | −0.789048 | − | 0.614331i | \(-0.789426\pi\) | ||
0.789048 | − | 0.614331i | \(-0.210574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7671.76 | − | 7671.76i | −0.917379 | − | 0.917379i | ||||
\(413\) | −598.710 | − | 598.710i | −0.0713331 | − | 0.0713331i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 11464.0i | − | 1.35113i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12861.4 | + | 12861.4i | −1.50496 | + | 1.50496i | ||||
\(419\) | 13243.2 | 1.54409 | 0.772044 | − | 0.635569i | \(-0.219234\pi\) | ||||
0.772044 | + | 0.635569i | \(0.219234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7488.37 | −0.866891 | −0.433445 | − | 0.901180i | \(-0.642702\pi\) | ||||
−0.433445 | + | 0.901180i | \(0.642702\pi\) | |||||||
\(422\) | 4248.69 | − | 4248.69i | 0.490102 | − | 0.490102i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 7714.83i | − | 0.883644i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1227.99 | − | 1227.99i | −0.139172 | − | 0.139172i | ||||
\(428\) | 234.970 | + | 234.970i | 0.0265367 | + | 0.0265367i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5842.63i | 0.652969i | 0.945202 | + | 0.326485i | \(0.105864\pi\) | ||||
−0.945202 | + | 0.326485i | \(0.894136\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5310.04 | − | 5310.04i | 0.589340 | − | 0.589340i | −0.348112 | − | 0.937453i | \(-0.613177\pi\) |
0.937453 | + | 0.348112i | \(0.113177\pi\) | |||||||
\(434\) | 671.934 | 0.0743177 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27062.1 | −2.97257 | ||||||||
\(437\) | 4437.70 | − | 4437.70i | 0.485776 | − | 0.485776i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10440.4i | − | 1.13506i | −0.823352 | − | 0.567530i | \(-0.807899\pi\) | ||
0.823352 | − | 0.567530i | \(-0.192101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2033.66 | − | 2033.66i | −0.218849 | − | 0.218849i | ||||
\(443\) | −2729.46 | − | 2729.46i | −0.292732 | − | 0.292732i | 0.545426 | − | 0.838159i | \(-0.316368\pi\) |
−0.838159 | + | 0.545426i | \(0.816368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4995.38i | 0.530355i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1587.57 | − | 1587.57i | 0.167423 | − | 0.167423i | ||||
\(449\) | −2227.63 | −0.234139 | −0.117070 | − | 0.993124i | \(-0.537350\pi\) | ||||
−0.117070 | + | 0.993124i | \(0.537350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14115.4 | 1.47377 | ||||||||
\(452\) | −13613.6 | + | 13613.6i | −1.41666 | + | 1.41666i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 17187.0i | − | 1.77670i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4328.64 | − | 4328.64i | −0.443075 | − | 0.443075i | 0.449969 | − | 0.893044i | \(-0.351435\pi\) |
−0.893044 | + | 0.449969i | \(0.851435\pi\) | |||||||
\(458\) | 9501.96 | + | 9501.96i | 0.969427 | + | 0.969427i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8223.98i | 0.830865i | 0.909624 | + | 0.415433i | \(0.136370\pi\) | ||||
−0.909624 | + | 0.415433i | \(0.863630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2611.01 | − | 2611.01i | 0.262082 | − | 0.262082i | −0.563817 | − | 0.825899i | \(-0.690668\pi\) |
0.825899 | + | 0.563817i | \(0.190668\pi\) | |||||||
\(464\) | −36170.2 | −3.61888 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12740.0 | −1.26646 | ||||||||
\(467\) | 12010.6 | − | 12010.6i | 1.19012 | − | 1.19012i | 0.213085 | − | 0.977034i | \(-0.431649\pi\) |
0.977034 | − | 0.213085i | \(-0.0683511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2737.29i | 0.269501i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14992.7 | − | 14992.7i | −1.46207 | − | 1.46207i | ||||
\(473\) | −10637.0 | − | 10637.0i | −1.03402 | − | 1.03402i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1060.03i | − | 0.102072i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14797.5 | − | 14797.5i | 1.41595 | − | 1.41595i | ||||
\(479\) | −6186.30 | −0.590103 | −0.295051 | − | 0.955481i | \(-0.595337\pi\) | ||||
−0.295051 | + | 0.955481i | \(0.595337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1677.10 | −0.158980 | ||||||||
\(482\) | −9171.42 | + | 9171.42i | −0.866694 | + | 0.866694i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15939.1i | 1.49691i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12791.1 | + | 12791.1i | 1.19019 | + | 1.19019i | 0.977015 | + | 0.213173i | \(0.0683797\pi\) |
0.213173 | + | 0.977015i | \(0.431620\pi\) | |||||||
\(488\) | −30750.9 | − | 30750.9i | −2.85251 | − | 2.85251i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13622.3i | − | 1.25207i | −0.779796 | − | 0.626034i | \(-0.784677\pi\) | ||
0.779796 | − | 0.626034i | \(-0.215323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2947.48 | + | 2947.48i | −0.269265 | + | 0.269265i | ||||
\(494\) | 10386.0 | 0.945931 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8863.68 | 0.802401 | ||||||||
\(497\) | 181.427 | − | 181.427i | 0.0163744 | − | 0.0163744i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15358.5i | 1.37784i | 0.724837 | + | 0.688920i | \(0.241915\pi\) | ||||
−0.724837 | + | 0.688920i | \(0.758085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17823.2 | + | 17823.2i | 1.58464 | + | 1.58464i | ||||
\(503\) | 9784.44 | + | 9784.44i | 0.867329 | + | 0.867329i | 0.992176 | − | 0.124847i | \(-0.0398440\pi\) |
−0.124847 | + | 0.992176i | \(0.539844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 20590.1i | − | 1.80898i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24530.4 | − | 24530.4i | 2.14244 | − | 2.14244i | ||||
\(509\) | −5300.61 | −0.461583 | −0.230791 | − | 0.973003i | \(-0.574131\pi\) | ||||
−0.230791 | + | 0.973003i | \(0.574131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2124.04 | 0.183879 | ||||||||
\(512\) | −9749.34 | + | 9749.34i | −0.841532 | + | 0.841532i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 8449.89i | − | 0.725114i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8155.41 | − | 8155.41i | −0.693761 | − | 0.693761i | ||||
\(518\) | −611.134 | − | 611.134i | −0.0518372 | − | 0.0518372i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8512.67i | 0.715829i | 0.933754 | + | 0.357915i | \(0.116512\pi\) | ||||
−0.933754 | + | 0.357915i | \(0.883488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7880.88 | + | 7880.88i | −0.658904 | + | 0.658904i | −0.955121 | − | 0.296217i | \(-0.904275\pi\) |
0.296217 | + | 0.955121i | \(0.404275\pi\) | |||||||
\(524\) | 4319.96 | 0.360149 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2688.02 | 0.222819 | ||||||||
\(527\) | 722.293 | − | 722.293i | 0.0597032 | − | 0.0597032i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5062.61i | − | 0.416093i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2706.82 | + | 2706.82i | 0.220593 | + | 0.220593i | ||||
\(533\) | −5699.33 | − | 5699.33i | −0.463162 | − | 0.463162i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 68546.4i | 5.52379i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14332.8 | + | 14332.8i | −1.14857 | + | 1.14857i | ||||
\(539\) | −15507.3 | −1.23923 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8961.43 | 0.712166 | 0.356083 | − | 0.934454i | \(-0.384112\pi\) | ||||
0.356083 | + | 0.934454i | \(0.384112\pi\) | |||||||
\(542\) | 2007.07 | − | 2007.07i | 0.159061 | − | 0.159061i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 8981.10i | − | 0.707833i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13458.8 | − | 13458.8i | −1.05203 | − | 1.05203i | −0.998570 | − | 0.0534553i | \(-0.982977\pi\) |
−0.0534553 | − | 0.998570i | \(-0.517023\pi\) | |||||||
\(548\) | 17639.0 | + | 17639.0i | 1.37500 | + | 1.37500i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15053.0i | − | 1.16385i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 519.296 | − | 519.296i | 0.0399325 | − | 0.0399325i | ||||
\(554\) | −8305.52 | −0.636946 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 50018.2 | 3.81519 | ||||||||
\(557\) | −12265.3 | + | 12265.3i | −0.933031 | + | 0.933031i | −0.997894 | − | 0.0648635i | \(-0.979339\pi\) |
0.0648635 | + | 0.997894i | \(0.479339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8589.74i | 0.649924i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12891.8 | + | 12891.8i | 0.967630 | + | 0.967630i | ||||
\(563\) | 10874.1 | + | 10874.1i | 0.814011 | + | 0.814011i | 0.985233 | − | 0.171222i | \(-0.0547714\pi\) |
−0.171222 | + | 0.985233i | \(0.554771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20433.2i | 1.51744i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4543.24 | − | 4543.24i | 0.335616 | − | 0.335616i | ||||
\(569\) | 5162.54 | 0.380360 | 0.190180 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190180 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6356.12 | 0.465842 | 0.232921 | − | 0.972496i | \(-0.425172\pi\) | ||||
0.232921 | + | 0.972496i | \(0.425172\pi\) | |||||||
\(572\) | 17232.7 | − | 17232.7i | 1.25968 | − | 1.25968i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 4153.66i | − | 0.302039i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7183.63 | + | 7183.63i | 0.518299 | + | 0.518299i | 0.917056 | − | 0.398758i | \(-0.130559\pi\) |
−0.398758 | + | 0.917056i | \(0.630559\pi\) | |||||||
\(578\) | 16819.3 | + | 16819.3i | 1.21037 | + | 1.21037i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3430.04i | − | 0.244926i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3923.66 | − | 3923.66i | 0.278733 | − | 0.278733i | ||||
\(584\) | 53189.6 | 3.76884 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32586.8 | −2.29718 | ||||||||
\(587\) | −6007.01 | + | 6007.01i | −0.422378 | + | 0.422378i | −0.886022 | − | 0.463644i | \(-0.846542\pi\) |
0.463644 | + | 0.886022i | \(0.346542\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3688.81i | 0.258055i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8061.64 | − | 8061.64i | −0.559681 | − | 0.559681i | ||||
\(593\) | −0.276387 | − | 0.276387i | −1.91397e−5 | − | 1.91397e-5i | 0.707097 | − | 0.707116i | \(-0.250004\pi\) |
−0.707116 | + | 0.707097i | \(0.750004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 30094.7i | − | 2.06833i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8313.59 | + | 8313.59i | −0.568509 | + | 0.568509i | ||||
\(599\) | −792.766 | −0.0540761 | −0.0270380 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270380 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6779.60 | −0.460142 | −0.230071 | − | 0.973174i | \(-0.573896\pi\) | ||||
−0.230071 | + | 0.973174i | \(0.573896\pi\) | |||||||
\(602\) | −3130.09 | + | 3130.09i | −0.211915 | + | 0.211915i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32440.3i | 2.18539i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14598.9 | + | 14598.9i | 0.976194 | + | 0.976194i | 0.999723 | − | 0.0235289i | \(-0.00749016\pi\) |
−0.0235289 | + | 0.999723i | \(0.507490\pi\) | |||||||
\(608\) | 22933.6 | + | 22933.6i | 1.52974 | + | 1.52974i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6585.76i | 0.436058i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9862.97 | + | 9862.97i | −0.649856 | + | 0.649856i | −0.952958 | − | 0.303102i | \(-0.901978\pi\) |
0.303102 | + | 0.952958i | \(0.401978\pi\) | |||||||
\(614\) | −23514.5 | −1.54555 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7558.17 | 0.494363 | ||||||||
\(617\) | −10135.5 | + | 10135.5i | −0.661329 | + | 0.661329i | −0.955693 | − | 0.294364i | \(-0.904892\pi\) |
0.294364 | + | 0.955693i | \(0.404892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27282.6i | 1.77153i | 0.464132 | + | 0.885766i | \(0.346366\pi\) | ||||
−0.464132 | + | 0.885766i | \(0.653634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30986.1 | − | 30986.1i | −1.99747 | − | 1.99747i | ||||
\(623\) | −1245.72 | − | 1245.72i | −0.0801106 | − | 0.0801106i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 35029.5i | − | 2.23652i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9180.22 | − | 9180.22i | 0.583329 | − | 0.583329i | ||||
\(629\) | −1313.87 | −0.0832869 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28414.9 | −1.79268 | −0.896340 | − | 0.443368i | \(-0.853783\pi\) | ||||
−0.896340 | + | 0.443368i | \(0.853783\pi\) | |||||||
\(632\) | 13004.1 | − | 13004.1i | 0.818471 | − | 0.818471i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24523.4i | 1.53620i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6261.33 | + | 6261.33i | 0.389455 | + | 0.389455i | ||||
\(638\) | −34921.5 | − | 34921.5i | −2.16702 | − | 2.16702i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26402.3i | 1.62688i | 0.581650 | + | 0.813439i | \(0.302407\pi\) | ||||
−0.581650 | + | 0.813439i | \(0.697593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2361.97 | − | 2361.97i | 0.144863 | − | 0.144863i | −0.630956 | − | 0.775819i | \(-0.717337\pi\) |
0.775819 | + | 0.630956i | \(0.217337\pi\) | |||||||
\(644\) | −4333.40 | −0.265155 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8136.61 | 0.495558 | ||||||||
\(647\) | 11204.5 | − | 11204.5i | 0.680826 | − | 0.680826i | −0.279360 | − | 0.960186i | \(-0.590122\pi\) |
0.960186 | + | 0.279360i | \(0.0901224\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15250.2i | − | 0.922377i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28812.7 | + | 28812.7i | 1.73066 | + | 1.73066i | ||||
\(653\) | −18407.7 | − | 18407.7i | −1.10314 | − | 1.10314i | −0.994030 | − | 0.109108i | \(-0.965201\pi\) |
−0.109108 | − | 0.994030i | \(-0.534799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 54792.0i | − | 3.26108i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2399.84 | + | 2399.84i | −0.142182 | + | 0.142182i | ||||
\(659\) | 8165.28 | 0.482662 | 0.241331 | − | 0.970443i | \(-0.422416\pi\) | ||||
0.241331 | + | 0.970443i | \(0.422416\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16725.1 | −0.984163 | −0.492082 | − | 0.870549i | \(-0.663764\pi\) | ||||
−0.492082 | + | 0.870549i | \(0.663764\pi\) | |||||||
\(662\) | 36221.9 | − | 36221.9i | 2.12659 | − | 2.12659i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 85894.2i | − | 5.02009i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12049.3 | + | 12049.3i | 0.699476 | + | 0.699476i | ||||
\(668\) | 22686.1 | + | 22686.1i | 1.31400 | + | 1.31400i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31279.0i | − | 1.79957i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −321.610 | + | 321.610i | −0.0184208 | + | 0.0184208i | −0.716257 | − | 0.697836i | \(-0.754146\pi\) |
0.697836 | + | 0.716257i | \(0.254146\pi\) | |||||||
\(674\) | −14330.9 | −0.819000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30223.4 | 1.71958 | ||||||||
\(677\) | −4497.58 | + | 4497.58i | −0.255326 | + | 0.255326i | −0.823150 | − | 0.567824i | \(-0.807785\pi\) |
0.567824 | + | 0.823150i | \(0.307785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3331.89i | 0.188316i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8557.68 | + | 8557.68i | 0.480485 | + | 0.480485i | ||||
\(683\) | 7479.00 | + | 7479.00i | 0.418999 | + | 0.418999i | 0.884859 | − | 0.465860i | \(-0.154255\pi\) |
−0.465860 | + | 0.884859i | \(0.654255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9215.30i | 0.512889i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −41289.9 | + | 41289.9i | −2.28803 | + | 2.28803i | ||||
\(689\) | −3168.48 | −0.175195 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22650.6 | −1.24699 | −0.623496 | − | 0.781827i | \(-0.714288\pi\) | ||||
−0.623496 | + | 0.781827i | \(0.714288\pi\) | |||||||
\(692\) | 33284.8 | − | 33284.8i | 1.82847 | − | 1.82847i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 52645.7i | − | 2.87955i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4464.96 | − | 4464.96i | −0.242643 | − | 0.242643i | ||||
\(698\) | −34702.7 | − | 34702.7i | −1.88183 | − | 1.88183i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1858.50i | − | 0.100135i | −0.998746 | − | 0.0500676i | \(-0.984056\pi\) | ||
0.998746 | − | 0.0500676i | \(-0.0159437\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3355.02 | − | 3355.02i | 0.179996 | − | 0.179996i | ||||
\(704\) | 40438.2 | 2.16487 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32517.6 | 1.73345 | ||||||||
\(707\) | 1842.82 | − | 1842.82i | 0.0980286 | − | 0.0980286i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14344.6i | 0.759836i | 0.925020 | + | 0.379918i | \(0.124048\pi\) | ||||
−0.925020 | + | 0.379918i | \(0.875952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31195.1 | − | 31195.1i | −1.64197 | − | 1.64197i | ||||
\(713\) | −2952.74 | − | 2952.74i | −0.155092 | − | 0.155092i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29117.9i | 1.51981i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22296.8 | − | 22296.8i | 1.15893 | − | 1.15893i | ||||
\(719\) | −10128.2 | −0.525337 | −0.262669 | − | 0.964886i | \(-0.584603\pi\) | ||||
−0.262669 | + | 0.964886i | \(0.584603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1381.92 | −0.0713807 | ||||||||
\(722\) | 4928.43 | − | 4928.43i | 0.254040 | − | 0.254040i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22506.4i | 1.15531i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15769.7 | − | 15769.7i | −0.804490 | − | 0.804490i | 0.179304 | − | 0.983794i | \(-0.442615\pi\) |
−0.983794 | + | 0.179304i | \(0.942615\pi\) | |||||||
\(728\) | −3051.74 | − | 3051.74i | −0.155364 | − | 0.155364i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6729.36i | 0.340485i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22982.0 | + | 22982.0i | −1.15806 | + | 1.15806i | −0.173169 | + | 0.984892i | \(0.555401\pi\) |
−0.984892 | + | 0.173169i | \(0.944599\pi\) | |||||||
\(734\) | 68611.5 | 3.45027 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36714.7 | −1.83875 | ||||||||
\(737\) | −34861.8 | + | 34861.8i | −1.74240 | + | 1.74240i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1989.79i | − | 0.0990467i | −0.998773 | − | 0.0495234i | \(-0.984230\pi\) | ||
0.998773 | − | 0.0495234i | \(-0.0157702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1154.59 | − | 1154.59i | −0.0571245 | − | 0.0571245i | ||||
\(743\) | 4460.57 | + | 4460.57i | 0.220246 | + | 0.220246i | 0.808602 | − | 0.588356i | \(-0.200225\pi\) |
−0.588356 | + | 0.808602i | \(0.700225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 48523.0i | − | 2.38144i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13500.4 | − | 13500.4i | 0.659924 | − | 0.659924i | ||||
\(749\) | 42.3254 | 0.00206480 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7038.34 | 0.341988 | 0.170994 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170994 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(752\) | −31657.0 | + | 31657.0i | −1.53512 | + | 1.53512i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28200.3i | 1.36206i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8036.02 | + | 8036.02i | 0.385831 | + | 0.385831i | 0.873198 | − | 0.487366i | \(-0.162042\pi\) |
−0.487366 | + | 0.873198i | \(0.662042\pi\) | |||||||
\(758\) | 918.304 | + | 918.304i | 0.0440031 | + | 0.0440031i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 11486.5i | − | 0.547154i | −0.961850 | − | 0.273577i | \(-0.911793\pi\) | ||
0.961850 | − | 0.273577i | \(-0.0882068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2437.36 | + | 2437.36i | −0.115647 | + | 0.115647i | ||||
\(764\) | −76899.0 | −3.64150 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33553.1 | −1.58267 | ||||||||
\(767\) | −6157.52 | + | 6157.52i | −0.289876 | + | 0.289876i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11244.4i | 0.527289i | 0.964620 | + | 0.263644i | \(0.0849245\pi\) | ||||
−0.964620 | + | 0.263644i | \(0.915075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36019.7 | + | 36019.7i | 1.67925 | + | 1.67925i | ||||
\(773\) | 21176.6 | + | 21176.6i | 0.985341 | + | 0.985341i | 0.999894 | − | 0.0145529i | \(-0.00463251\pi\) |
−0.0145529 | + | 0.999894i | \(0.504633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 83436.4i | 3.85978i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16599.6 | + | 16599.6i | −0.764942 | + | 0.764942i | ||||
\(779\) | 22802.9 | 1.04878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4621.26 | 0.211731 | ||||||||
\(782\) | −6513.02 | + | 6513.02i | −0.297833 | + | 0.297833i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 60195.0i | 2.74212i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1608.25 | + | 1608.25i | 0.0728437 | + | 0.0728437i | 0.742590 | − | 0.669746i | \(-0.233597\pi\) |
−0.669746 | + | 0.742590i | \(0.733597\pi\) | |||||||
\(788\) | 44643.3 | + | 44643.3i | 2.01821 | + | 2.01821i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2452.24i | 0.110229i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12629.4 | + | 12629.4i | −0.565553 | + | 0.565553i | ||||
\(794\) | −35874.3 | −1.60344 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28558.0 | 1.27162 | ||||||||
\(797\) | 7418.34 | − | 7418.34i | 0.329700 | − | 0.329700i | −0.522772 | − | 0.852472i | \(-0.675102\pi\) |
0.852472 | + | 0.522772i | \(0.175102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5159.41i | 0.228444i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16946.6 | − | 16946.6i | −0.746142 | − | 0.746142i | ||||
\(803\) | 27051.5 | + | 27051.5i | 1.18883 | + | 1.18883i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6910.61i | − | 0.302005i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 46147.3 | − | 46147.3i | 2.00923 | − | 2.00923i | ||||
\(809\) | −1490.14 | −0.0647595 | −0.0323797 | − | 0.999476i | \(-0.510309\pi\) | ||||
−0.0323797 | + | 0.999476i | \(0.510309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26161.5 | 1.13274 | 0.566371 | − | 0.824150i | \(-0.308347\pi\) | ||||
0.566371 | + | 0.824150i | \(0.308347\pi\) | |||||||
\(812\) | −7349.59 | + | 7349.59i | −0.317636 | + | 0.317636i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 15566.7i | − | 0.670284i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17183.7 | − | 17183.7i | −0.735839 | − | 0.735839i | ||||
\(818\) | −38087.7 | − | 38087.7i | −1.62800 | − | 1.62800i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21056.4i | 0.895095i | 0.894260 | + | 0.447548i | \(0.147702\pi\) | ||||
−0.894260 | + | 0.447548i | \(0.852298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −187.614 | + | 187.614i | −0.00794631 | + | 0.00794631i | −0.711069 | − | 0.703122i | \(-0.751789\pi\) |
0.703122 | + | 0.711069i | \(0.251789\pi\) | |||||||
\(824\) | −34605.7 | −1.46304 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4487.59 | −0.189035 | ||||||||
\(827\) | 10888.3 | − | 10888.3i | 0.457827 | − | 0.457827i | −0.440114 | − | 0.897942i | \(-0.645062\pi\) |
0.897942 | + | 0.440114i | \(0.145062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9441.85i | − | 0.395572i | −0.980245 | − | 0.197786i | \(-0.936625\pi\) | ||
0.980245 | − | 0.197786i | \(-0.0633751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16327.6 | − | 16327.6i | −0.680357 | − | 0.680357i | ||||
\(833\) | 4905.24 | + | 4905.24i | 0.204029 | + | 0.204029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 68947.5i | 2.85239i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49631.8 | − | 49631.8i | 2.04594 | − | 2.04594i | ||||
\(839\) | 25744.3 | 1.05935 | 0.529673 | − | 0.848202i | \(-0.322315\pi\) | ||||
0.529673 | + | 0.848202i | \(0.322315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16483.1 | 0.675840 | ||||||||
\(842\) | −28064.3 | + | 28064.3i | −1.14865 | + | 1.14865i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 22776.3i | − | 0.928903i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1435.56 | + | 1435.56i | 0.0582367 | + | 0.0582367i | ||||
\(848\) | −15230.5 | − | 15230.5i | −0.616768 | − | 0.616768i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5371.11i | 0.216356i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32181.0 | − | 32181.0i | 1.29174 | − | 1.29174i | 0.358033 | − | 0.933709i | \(-0.383448\pi\) |
0.933709 | − | 0.358033i | \(-0.116552\pi\) | |||||||
\(854\) | −9204.28 | −0.368810 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1059.90 | 0.0423208 | ||||||||
\(857\) | 15272.0 | − | 15272.0i | 0.608729 | − | 0.608729i | −0.333885 | − | 0.942614i | \(-0.608360\pi\) |
0.942614 | + | 0.333885i | \(0.108360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 11140.0i | − | 0.442484i | −0.975219 | − | 0.221242i | \(-0.928989\pi\) | ||
0.975219 | − | 0.221242i | \(-0.0710110\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21896.5 | + | 21896.5i | 0.865196 | + | 0.865196i | ||||
\(863\) | −2425.86 | − | 2425.86i | −0.0956863 | − | 0.0956863i | 0.657643 | − | 0.753330i | \(-0.271553\pi\) |
−0.753330 | + | 0.657643i | \(0.771553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 39801.0i | − | 1.56177i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1801.05 | − | 1801.05i | 0.0704282 | − | 0.0704282i | ||||
\(869\) | 13227.4 | 0.516350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28152.0 | 1.09517 | ||||||||
\(872\) | −61035.7 | + | 61035.7i | −2.37033 | + | 2.37033i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 33262.5i | − | 1.28732i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28777.5 | − | 28777.5i | −1.10803 | − | 1.10803i | −0.993409 | − | 0.114625i | \(-0.963433\pi\) |
−0.114625 | − | 0.993409i | \(-0.536567\pi\) | |||||||
\(878\) | −39127.5 | − | 39127.5i | −1.50397 | − | 1.50397i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3701.33i | 0.141545i | 0.997492 | + | 0.0707724i | \(0.0225464\pi\) | ||||
−0.997492 | + | 0.0707724i | \(0.977454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30772.1 | + | 30772.1i | −1.17278 | + | 1.17278i | −0.191236 | + | 0.981544i | \(0.561249\pi\) |
−0.981544 | + | 0.191236i | \(0.938751\pi\) | |||||||
\(884\) | −10902.0 | −0.414790 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20458.4 | −0.775750 | ||||||||
\(887\) | 12139.6 | − | 12139.6i | 0.459536 | − | 0.459536i | −0.438967 | − | 0.898503i | \(-0.644656\pi\) |
0.898503 | + | 0.438967i | \(0.144656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4418.69i | − | 0.166702i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13389.6 | + | 13389.6i | 0.502598 | + | 0.502598i | ||||
\(893\) | −13174.7 | − | 13174.7i | −0.493702 | − | 0.493702i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2982.15i | − | 0.111190i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8348.53 | + | 8348.53i | −0.310238 | + | 0.310238i | ||||
\(899\) | −10015.9 | −0.371578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2482.25 | −0.0917821 | ||||||||
\(902\) | 52900.5 | − | 52900.5i | 1.95276 | − | 1.95276i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 61408.2i | 2.25930i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 316.892 | + | 316.892i | 0.0116011 | + | 0.0116011i | 0.712884 | − | 0.701282i | \(-0.247389\pi\) |
−0.701282 | + | 0.712884i | \(0.747389\pi\) | |||||||
\(908\) | −46067.8 | − | 46067.8i | −1.68372 | − | 1.68372i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15635.7i | 0.568643i | 0.958729 | + | 0.284321i | \(0.0917683\pi\) | ||||
−0.958729 | + | 0.284321i | \(0.908232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43684.6 | − | 43684.6i | 1.58352 | − | 1.58352i | ||||
\(914\) | −32445.0 | −1.17416 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50938.1 | 1.83738 | ||||||||
\(917\) | 389.080 | − | 389.080i | 0.0140115 | − | 0.0140115i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7430.80i | 0.266724i | 0.991067 | + | 0.133362i | \(0.0425773\pi\) | ||||
−0.991067 | + | 0.133362i | \(0.957423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30821.1 | + | 30821.1i | 1.10091 | + | 1.10091i | ||||
\(923\) | −1865.91 | − | 1865.91i | −0.0665408 | − | 0.0665408i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 19570.6i | − | 0.694526i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −62269.5 | + | 62269.5i | −2.20269 | + | 2.20269i | ||||
\(929\) | −889.629 | −0.0314185 | −0.0157092 | − | 0.999877i | \(-0.505001\pi\) | ||||
−0.0157092 | + | 0.999877i | \(0.505001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25051.4 | −0.881876 | ||||||||
\(932\) | −34148.2 | + | 34148.2i | −1.20017 | + | 1.20017i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 90024.8i | − | 3.15386i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4028.44 | + | 4028.44i | 0.140452 | + | 0.140452i | 0.773837 | − | 0.633385i | \(-0.218335\pi\) |
−0.633385 | + | 0.773837i | \(0.718335\pi\) | |||||||
\(938\) | 10258.6 | + | 10258.6i | 0.357094 | + | 0.357094i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14232.9i | 0.493072i | 0.969134 | + | 0.246536i | \(0.0792924\pi\) | ||||
−0.969134 | + | 0.246536i | \(0.920708\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18252.7 | + | 18252.7i | −0.630319 | + | 0.630319i | ||||
\(944\) | −59197.0 | −2.04099 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −79729.0 | −2.74018 | ||||||||
\(947\) | −13637.1 | + | 13637.1i | −0.467947 | + | 0.467947i | −0.901249 | − | 0.433302i | \(-0.857348\pi\) |
0.433302 | + | 0.901249i | \(0.357348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 21845.0i | − | 0.747227i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2390.79 | − | 2390.79i | −0.0813927 | − | 0.0813927i | ||||
\(953\) | 10234.2 | + | 10234.2i | 0.347869 | + | 0.347869i | 0.859315 | − | 0.511446i | \(-0.170890\pi\) |
−0.511446 | + | 0.859315i | \(0.670890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 79326.5i | − | 2.68368i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23184.5 | + | 23184.5i | −0.781896 | + | 0.781896i | ||||
\(959\) | 3177.33 | 0.106988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27336.6 | −0.917611 | ||||||||
\(962\) | −6285.29 | + | 6285.29i | −0.210651 | + | 0.210651i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 49166.1i | 1.64267i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7178.73 | − | 7178.73i | −0.238731 | − | 0.238731i | 0.577594 | − | 0.816324i | \(-0.303992\pi\) |
−0.816324 | + | 0.577594i | \(0.803992\pi\) | |||||||
\(968\) | 35948.9 | + | 35948.9i | 1.19364 | + | 1.19364i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43718.0i | 1.44488i | 0.691434 | + | 0.722440i | \(0.256979\pi\) | ||||
−0.691434 | + | 0.722440i | \(0.743021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4504.92 | − | 4504.92i | 0.148429 | − | 0.148429i | ||||
\(974\) | 95875.0 | 3.15404 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −121416. | −3.98201 | ||||||||
\(977\) | 36446.0 | − | 36446.0i | 1.19346 | − | 1.19346i | 0.217371 | − | 0.976089i | \(-0.430252\pi\) |
0.976089 | − | 0.217371i | \(-0.0697482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31730.8i | − | 1.03587i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51052.5 | − | 51052.5i | −1.65901 | − | 1.65901i | ||||
\(983\) | −28612.6 | − | 28612.6i | −0.928382 | − | 0.928382i | 0.0692194 | − | 0.997601i | \(-0.477949\pi\) |
−0.997601 | + | 0.0692194i | \(0.977949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22092.6i | 0.713562i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27838.7 | − | 27838.7i | 0.896424 | − | 0.896424i | ||||
\(989\) | 27509.6 | 0.884485 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56452.4 | 1.80956 | 0.904778 | − | 0.425884i | \(-0.140037\pi\) | ||||
0.904778 | + | 0.425884i | \(0.140037\pi\) | |||||||
\(992\) | 15259.4 | − | 15259.4i | 0.488394 | − | 0.488394i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1359.87i | − | 0.0433928i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19121.4 | − | 19121.4i | −0.607402 | − | 0.607402i | 0.334864 | − | 0.942266i | \(-0.391310\pi\) |
−0.942266 | + | 0.334864i | \(0.891310\pi\) | |||||||
\(998\) | 57559.4 | + | 57559.4i | 1.82566 | + | 1.82566i | ||||
\(999\) | 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 | 225.4.f.c.107.6 | 12 | ||
3.2 | odd | 2 | inner | 225.4.f.c.107.1 | 12 | ||
5.2 | odd | 4 | 45.4.f.a.8.6 | yes | 12 | ||
5.3 | odd | 4 | inner | 225.4.f.c.143.1 | 12 | ||
5.4 | even | 2 | 45.4.f.a.17.1 | yes | 12 | ||
15.2 | even | 4 | 45.4.f.a.8.1 | ✓ | 12 | ||
15.8 | even | 4 | inner | 225.4.f.c.143.6 | 12 | ||
15.14 | odd | 2 | 45.4.f.a.17.6 | yes | 12 | ||
20.7 | even | 4 | 720.4.w.d.593.4 | 12 | |||
20.19 | odd | 2 | 720.4.w.d.17.3 | 12 | |||
60.47 | odd | 4 | 720.4.w.d.593.3 | 12 | |||
60.59 | even | 2 | 720.4.w.d.17.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.f.a.8.1 | ✓ | 12 | 15.2 | even | 4 | ||
45.4.f.a.8.6 | yes | 12 | 5.2 | odd | 4 | ||
45.4.f.a.17.1 | yes | 12 | 5.4 | even | 2 | ||
45.4.f.a.17.6 | yes | 12 | 15.14 | odd | 2 | ||
225.4.f.c.107.1 | 12 | 3.2 | odd | 2 | inner | ||
225.4.f.c.107.6 | 12 | 1.1 | even | 1 | trivial | ||
225.4.f.c.143.1 | 12 | 5.3 | odd | 4 | inner | ||
225.4.f.c.143.6 | 12 | 15.8 | even | 4 | inner | ||
720.4.w.d.17.3 | 12 | 20.19 | odd | 2 | |||
720.4.w.d.17.4 | 12 | 60.59 | even | 2 | |||
720.4.w.d.593.3 | 12 | 60.47 | odd | 4 | |||
720.4.w.d.593.4 | 12 | 20.7 | even | 4 |