Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.4.i.k.541.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.0000 | + | 19.0526i | 0.593944 | + | 1.02874i | 0.993695 | + | 0.112118i | \(0.0357633\pi\) |
−0.399751 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50000 | + | 7.79423i | 0.123346 | + | 0.213641i | 0.921085 | − | 0.389362i | \(-0.127304\pi\) |
−0.797739 | + | 0.603002i | \(0.793971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.50000 | + | 14.7224i | −0.181344 | + | 0.314098i | −0.942339 | − | 0.334661i | \(-0.891378\pi\) |
0.760994 | + | 0.648759i | \(0.224712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −75.0000 | −1.07001 | −0.535005 | − | 0.844849i | \(-0.679690\pi\) | ||||
−0.535005 | + | 0.844849i | \(0.679690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.0482980 | −0.0241490 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241490 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −91.5000 | + | 158.483i | −0.829525 | + | 1.43678i | 0.0688868 | + | 0.997624i | \(0.478055\pi\) |
−0.898412 | + | 0.439155i | \(0.855278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −64.5000 | − | 111.717i | −0.413012 | − | 0.715358i | 0.582205 | − | 0.813042i | \(-0.302190\pi\) |
−0.995217 | + | 0.0976839i | \(0.968857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 93.5000 | − | 161.947i | 0.541713 | − | 0.938274i | −0.457093 | − | 0.889419i | \(-0.651109\pi\) |
0.998806 | − | 0.0488552i | \(-0.0155573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 110.000 | 0.531240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.0000 | −0.151069 | −0.0755347 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755347 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −132.000 | + | 228.631i | −0.502803 | + | 0.870881i | 0.497191 | + | 0.867641i | \(0.334365\pi\) |
−0.999995 | + | 0.00324004i | \(0.998969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −221.500 | − | 383.649i | −0.785545 | − | 1.36060i | −0.928673 | − | 0.370900i | \(-0.879049\pi\) |
0.143128 | − | 0.989704i | \(-0.454284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −304.500 | − | 527.409i | −0.945019 | − | 1.63682i | −0.755713 | − | 0.654903i | \(-0.772710\pi\) |
−0.189306 | − | 0.981918i | \(-0.560624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −70.5000 | + | 122.110i | −0.205539 | + | 0.356005i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −228.000 | −0.590910 | −0.295455 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295455 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.0000 | 0.110324 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −30.0000 | + | 51.9615i | −0.0661978 | + | 0.114658i | −0.897225 | − | 0.441574i | \(-0.854420\pi\) |
0.831027 | + | 0.556232i | \(0.187753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 227.000 | + | 393.176i | 0.476465 | + | 0.825262i | 0.999636 | − | 0.0269658i | \(-0.00858452\pi\) |
−0.523171 | + | 0.852228i | \(0.675251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42.5000 | + | 73.6122i | 0.0810996 | + | 0.140469i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 122.000 | − | 211.310i | 0.222458 | − | 0.385308i | −0.733096 | − | 0.680125i | \(-0.761925\pi\) |
0.955554 | + | 0.294817i | \(0.0952587\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 444.000 | 0.742156 | 0.371078 | − | 0.928602i | \(-0.378988\pi\) | ||||
0.371078 | + | 0.928602i | \(0.378988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 398.000 | 0.638115 | 0.319057 | − | 0.947735i | \(-0.396634\pi\) | ||||
0.319057 | + | 0.947735i | \(0.396634\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −99.0000 | + | 171.473i | −0.146521 | + | 0.253781i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 174.500 | + | 302.243i | 0.248516 | + | 0.430443i | 0.963114 | − | 0.269092i | \(-0.0867237\pi\) |
−0.714598 | + | 0.699535i | \(0.753390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −519.000 | − | 898.934i | −0.686357 | − | 1.18881i | −0.973008 | − | 0.230771i | \(-0.925875\pi\) |
0.286651 | − | 0.958035i | \(-0.407458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −187.500 | + | 324.760i | −0.239262 | + | 0.414413i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 852.000 | 1.01474 | 0.507370 | − | 0.861728i | \(-0.330618\pi\) | ||||
0.507370 | + | 0.861728i | \(0.330618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −374.000 | −0.430834 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0000 | + | 17.3205i | −0.0107998 | + | 0.0187058i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −457.000 | − | 791.547i | −0.478364 | − | 0.828551i | 0.521328 | − | 0.853356i | \(-0.325437\pi\) |
−0.999692 | + | 0.0248053i | \(0.992103\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −577.500 | − | 1000.26i | −0.568945 | − | 0.985441i | −0.996671 | − | 0.0815325i | \(-0.974019\pi\) |
0.427726 | − | 0.903908i | \(-0.359315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 287.000 | − | 497.099i | 0.274553 | − | 0.475540i | −0.695469 | − | 0.718556i | \(-0.744803\pi\) |
0.970022 | + | 0.243016i | \(0.0781368\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 294.000 | 0.265627 | 0.132813 | − | 0.991141i | \(-0.457599\pi\) | ||||
0.132813 | + | 0.991141i | \(0.457599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −340.000 | −0.298772 | −0.149386 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149386 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −340.500 | + | 589.763i | −0.283465 | + | 0.490976i | −0.972236 | − | 0.234003i | \(-0.924817\pi\) |
0.688771 | + | 0.724979i | \(0.258151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 457.500 | + | 792.413i | 0.370975 | + | 0.642547i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −825.000 | − | 1428.94i | −0.635526 | − | 1.10076i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 625.000 | − | 1082.53i | 0.469572 | − | 0.813322i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 578.000 | 0.403852 | 0.201926 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201926 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 391.500 | − | 678.098i | 0.261111 | − | 0.452257i | −0.705427 | − | 0.708783i | \(-0.749245\pi\) |
0.966537 | + | 0.256526i | \(0.0825779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −44.0000 | − | 76.2102i | −0.0286863 | − | 0.0496862i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −117.000 | − | 202.650i | −0.0729634 | − | 0.126376i | 0.827235 | − | 0.561855i | \(-0.189912\pi\) |
−0.900199 | + | 0.435479i | \(0.856579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1585.00 | + | 2745.30i | −0.967179 | + | 1.67520i | −0.263538 | + | 0.964649i | \(0.584889\pi\) |
−0.703642 | + | 0.710555i | \(0.748444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −153.000 | −0.0894720 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −645.000 | −0.369409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 631.500 | − | 1093.79i | 0.347211 | − | 0.601388i | −0.638542 | − | 0.769587i | \(-0.720462\pi\) |
0.985753 | + | 0.168200i | \(0.0537953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −425.500 | − | 736.988i | −0.229316 | − | 0.397187i | 0.728290 | − | 0.685269i | \(-0.240316\pi\) |
−0.957606 | + | 0.288083i | \(0.906982\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −467.500 | − | 809.734i | −0.242261 | − | 0.419609i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1139.50 | + | 1973.67i | −0.579248 | + | 1.00329i | 0.416317 | + | 0.909219i | \(0.363321\pi\) |
−0.995566 | + | 0.0940683i | \(0.970013\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4026.00 | −1.97077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1297.00 | −0.623245 | −0.311622 | − | 0.950206i | \(-0.600872\pi\) | ||||
−0.311622 | + | 0.950206i | \(0.600872\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −162.000 | + | 280.592i | −0.0750655 | + | 0.130017i | −0.901115 | − | 0.433581i | \(-0.857250\pi\) |
0.826049 | + | 0.563598i | \(0.190583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 954.000 | + | 1652.38i | 0.434228 | + | 0.752106i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 87.0000 | + | 150.688i | 0.0382340 | + | 0.0662233i | 0.884509 | − | 0.466523i | \(-0.154493\pi\) |
−0.846275 | + | 0.532746i | \(0.821160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 275.000 | − | 476.314i | 0.118789 | − | 0.205748i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4596.00 | −1.91911 | −0.959556 | − | 0.281517i | \(-0.909163\pi\) | ||||
−0.959556 | + | 0.281517i | \(0.909163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 548.000 | 0.225042 | 0.112521 | − | 0.993649i | \(-0.464108\pi\) | ||||
0.112521 | + | 0.993649i | \(0.464108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −85.0000 | + | 147.224i | −0.0337801 | + | 0.0585089i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −337.500 | − | 584.567i | −0.131981 | − | 0.228598i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2319.00 | − | 4016.63i | −0.878518 | − | 1.52164i | −0.852967 | − | 0.521964i | \(-0.825199\pi\) |
−0.0255508 | − | 0.999674i | \(-0.508134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1721.00 | − | 2980.86i | 0.641867 | − | 1.11175i | −0.343149 | − | 0.939281i | \(-0.611494\pi\) |
0.985016 | − | 0.172465i | \(-0.0551731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3312.00 | −1.19782 | −0.598909 | − | 0.800817i | \(-0.704399\pi\) | ||||
−0.598909 | + | 0.800817i | \(0.704399\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1745.00 | 0.621607 | 0.310803 | − | 0.950474i | \(-0.399402\pi\) | ||||
0.310803 | + | 0.950474i | \(0.399402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1419.00 | − | 2457.78i | 0.490612 | − | 0.849765i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 660.000 | + | 1143.15i | 0.224860 | + | 0.389470i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0000 | − | 31.1769i | −0.00595735 | − | 0.0103184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1679.00 | − | 2908.11i | 0.547806 | − | 0.948828i | −0.450618 | − | 0.892717i | \(-0.648796\pi\) |
0.998425 | − | 0.0561116i | \(-0.0178702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2215.00 | −0.702613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4114.00 | 1.28699 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 637.500 | − | 1104.18i | 0.194040 | − | 0.336088i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1756.00 | − | 3041.48i | −0.527311 | − | 0.913330i | −0.999493 | − | 0.0318291i | \(-0.989867\pi\) |
0.472182 | − | 0.881501i | \(-0.343467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1056.00 | − | 1829.05i | −0.308763 | − | 0.534793i | 0.669329 | − | 0.742966i | \(-0.266582\pi\) |
−0.978092 | + | 0.208173i | \(0.933248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1450.00 | + | 2511.47i | −0.418422 | + | 0.724729i | −0.995781 | − | 0.0917620i | \(-0.970750\pi\) |
0.577359 | + | 0.816491i | \(0.304083\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5178.00 | −1.45589 | −0.727944 | − | 0.685636i | \(-0.759524\pi\) | ||||
−0.727944 | + | 0.685636i | \(0.759524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3045.00 | −0.845251 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2505.00 | + | 4338.79i | −0.677971 | + | 1.17428i | 0.297620 | + | 0.954684i | \(0.403807\pi\) |
−0.975591 | + | 0.219595i | \(0.929526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2601.50 | + | 4505.93i | 0.695342 | + | 1.20437i | 0.970065 | + | 0.242844i | \(0.0780803\pi\) |
−0.274724 | + | 0.961523i | \(0.588586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 352.500 | + | 610.548i | 0.0919200 | + | 0.159210i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.0000 | − | 58.8897i | 0.00875858 | − | 0.0151703i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −549.000 | −0.138058 | −0.0690290 | − | 0.997615i | \(-0.521990\pi\) | ||||
−0.0690290 | + | 0.997615i | \(0.521990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1647.00 | −0.409273 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3547.50 | − | 6144.45i | 0.861039 | − | 1.49136i | −0.00988853 | − | 0.999951i | \(-0.503148\pi\) |
0.870927 | − | 0.491412i | \(-0.163519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −374.000 | − | 647.787i | −0.0897268 | − | 0.155411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2142.00 | − | 3710.05i | −0.502211 | − | 0.869854i | −0.999997 | − | 0.00255442i | \(-0.999187\pi\) |
0.497786 | − | 0.867300i | \(-0.334146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −570.000 | + | 987.269i | −0.132131 | + | 0.228858i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6669.00 | −1.51158 | −0.755792 | − | 0.654812i | \(-0.772748\pi\) | ||||
−0.755792 | + | 0.654812i | \(0.772748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5560.00 | −1.24630 | −0.623148 | − | 0.782104i | \(-0.714146\pi\) | ||||
−0.623148 | + | 0.782104i | \(0.714146\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 112.500 | − | 194.856i | 0.0246691 | − | 0.0427282i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3367.00 | − | 5831.82i | −0.730337 | − | 1.26498i | −0.956739 | − | 0.290947i | \(-0.906030\pi\) |
0.226402 | − | 0.974034i | \(-0.427304\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3855.00 | + | 6677.06i | 0.818399 | + | 1.41751i | 0.906862 | + | 0.421429i | \(0.138471\pi\) |
−0.0884630 | + | 0.996079i | \(0.528195\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2368.00 | + | 4101.50i | −0.497396 | + | 0.861515i | −0.999995 | − | 0.00300456i | \(-0.999044\pi\) |
0.502600 | + | 0.864519i | \(0.332377\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5808.00 | −1.19455 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 712.000 | 0.144922 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2775.00 | − | 4806.44i | 0.553301 | − | 0.958346i | −0.444732 | − | 0.895663i | \(-0.646701\pi\) |
0.998034 | − | 0.0626822i | \(-0.0199654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 150.000 | + | 259.808i | 0.0296045 | + | 0.0512766i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1555.50 | − | 2694.21i | −0.300859 | − | 0.521103i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4873.00 | − | 8440.28i | 0.933140 | − | 1.61625i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2270.00 | 0.426163 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5663.00 | 1.05278 | 0.526392 | − | 0.850242i | \(-0.323545\pi\) | ||||
0.526392 | + | 0.850242i | \(0.323545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 960.000 | − | 1662.77i | 0.175037 | − | 0.303174i | −0.765137 | − | 0.643868i | \(-0.777329\pi\) |
0.940174 | + | 0.340694i | \(0.110662\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1408.00 | − | 2438.73i | −0.254265 | − | 0.440399i | 0.710431 | − | 0.703767i | \(-0.248500\pi\) |
−0.964696 | + | 0.263368i | \(0.915167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2892.00 | − | 5009.09i | −0.512400 | − | 0.887503i | −0.999897 | − | 0.0143783i | \(-0.995423\pi\) |
0.487496 | − | 0.873125i | \(-0.337910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 580.500 | − | 1005.46i | 0.101886 | − | 0.176472i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 300.000 | 0.0516794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 425.000 | 0.0725377 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6699.00 | − | 11603.0i | 1.12258 | − | 1.94436i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2177.00 | + | 3770.67i | 0.361507 | + | 0.626148i | 0.988209 | − | 0.153111i | \(-0.0489291\pi\) |
−0.626702 | + | 0.779259i | \(0.715596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −610.000 | − | 1056.55i | −0.0994861 | − | 0.172315i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1948.00 | + | 3374.03i | −0.314879 | + | 0.545387i | −0.979412 | − | 0.201872i | \(-0.935297\pi\) |
0.664533 | + | 0.747259i | \(0.268631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1683.00 | 0.267271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4444.00 | 0.699573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3804.00 | + | 6588.72i | −0.588500 | + | 1.01931i | 0.405929 | + | 0.913904i | \(0.366948\pi\) |
−0.994429 | + | 0.105407i | \(0.966385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2143.00 | − | 3711.78i | −0.328688 | − | 0.569305i | 0.653564 | − | 0.756872i | \(-0.273273\pi\) |
−0.982252 | + | 0.187567i | \(0.939940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1453.50 | − | 2517.54i | −0.219156 | − | 0.379589i | 0.735394 | − | 0.677639i | \(-0.236997\pi\) |
−0.954550 | + | 0.298050i | \(0.903664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1110.00 | − | 1922.58i | 0.165951 | − | 0.287436i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5988.00 | 0.880319 | 0.440160 | − | 0.897920i | \(-0.354922\pi\) | ||||
0.440160 | + | 0.897920i | \(0.354922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6843.00 | −0.997667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 995.000 | − | 1723.39i | 0.142687 | − | 0.247141i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1607.00 | + | 2783.41i | 0.228569 | + | 0.395893i | 0.957384 | − | 0.288818i | \(-0.0932621\pi\) |
−0.728815 | + | 0.684710i | \(0.759929\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2508.00 | − | 4343.98i | −0.350967 | − | 0.607893i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4709.50 | + | 8157.09i | −0.653750 | + | 1.13233i | 0.328456 | + | 0.944519i | \(0.393472\pi\) |
−0.982206 | + | 0.187809i | \(0.939862\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2193.00 | 0.299590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4544.00 | 0.615856 | 0.307928 | − | 0.951410i | \(-0.400364\pi\) | ||||
0.307928 | + | 0.951410i | \(0.400364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5743.50 | + | 9948.03i | −0.766264 | + | 1.32721i | 0.173312 | + | 0.984867i | \(0.444553\pi\) |
−0.939576 | + | 0.342341i | \(0.888780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 495.000 | + | 857.365i | 0.0655261 | + | 0.113494i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3922.50 | − | 6793.97i | −0.511256 | − | 0.885522i | −0.999915 | − | 0.0130466i | \(-0.995847\pi\) |
0.488659 | − | 0.872475i | \(-0.337486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6862.50 | − | 11886.2i | 0.887600 | − | 1.53737i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1745.00 | 0.222280 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4133.00 | 0.522492 | 0.261246 | − | 0.965272i | \(-0.415867\pi\) | ||||
0.261246 | + | 0.965272i | \(0.415867\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1662.00 | + | 2878.67i | −0.206973 | + | 0.358488i | −0.950760 | − | 0.309929i | \(-0.899695\pi\) |
0.743786 | + | 0.668417i | \(0.233028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1589.50 | + | 2753.09i | 0.196473 | + | 0.340301i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −153.000 | − | 265.004i | −0.0186337 | − | 0.0322746i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −935.500 | + | 1620.33i | −0.113099 | + | 0.195893i | −0.917018 | − | 0.398845i | \(-0.869411\pi\) |
0.803919 | + | 0.594738i | \(0.202744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1320.00 | −0.157271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5190.00 | −0.613897 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2704.50 | + | 4684.33i | −0.315330 | + | 0.546168i | −0.979508 | − | 0.201407i | \(-0.935449\pi\) |
0.664177 | + | 0.747575i | \(0.268782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6542.00 | + | 11331.1i | 0.757334 | + | 1.31174i | 0.944206 | + | 0.329356i | \(0.106832\pi\) |
−0.186872 | + | 0.982384i | \(0.559835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 937.500 | + | 1623.80i | 0.107001 | + | 0.185331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4994.00 | + | 8649.86i | −0.565987 | + | 0.980319i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7848.00 | −0.877088 | −0.438544 | − | 0.898710i | \(-0.644506\pi\) | ||||
−0.438544 | + | 0.898710i | \(0.644506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10222.0 | −1.13450 | −0.567249 | − | 0.823546i | \(-0.691992\pi\) | ||||
−0.567249 | + | 0.823546i | \(0.691992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 366.000 | − | 633.931i | 0.0400644 | − | 0.0693936i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2836.00 | − | 4912.10i | −0.308326 | − | 0.534035i | 0.669671 | − | 0.742658i | \(-0.266435\pi\) |
−0.977996 | + | 0.208623i | \(0.933102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −222.000 | − | 384.515i | −0.0238093 | − | 0.0412390i | 0.853875 | − | 0.520478i | \(-0.174246\pi\) |
−0.877685 | + | 0.479239i | \(0.840913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2130.00 | − | 3689.27i | 0.226903 | − | 0.393007i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10434.0 | 1.09668 | 0.548342 | − | 0.836254i | \(-0.315259\pi\) | ||||
0.548342 | + | 0.836254i | \(0.315259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2376.00 | −0.248074 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −935.000 | + | 1619.47i | −0.0963373 | + | 0.166861i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5590.00 | − | 9682.16i | −0.572186 | − | 0.991056i | −0.996341 | − | 0.0854661i | \(-0.972762\pi\) |
0.424155 | − | 0.905590i | \(-0.360571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7509.00 | − | 13006.0i | −0.758631 | − | 1.31399i | −0.943549 | − | 0.331234i | \(-0.892535\pi\) |
0.184917 | − | 0.982754i | \(-0.440798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8083.00 | + | 14000.2i | −0.811337 | + | 1.40528i | 0.100592 | + | 0.994928i | \(0.467926\pi\) |
−0.911929 | + | 0.410349i | \(0.865407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2964.00 | 0.293699 | 0.146850 | − | 0.989159i | \(-0.453087\pi\) | ||||
0.146850 | + | 0.989159i | \(0.453087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5368.00 | 0.528510 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1993.50 | − | 3452.84i | 0.193787 | − | 0.335649i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 50.0000 | + | 86.6025i | 0.00482980 | + | 0.00836547i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2706.00 | + | 4686.93i | 0.258122 | + | 0.447080i | 0.965739 | − | 0.259516i | \(-0.0835631\pi\) |
−0.707617 | + | 0.706596i | \(0.750230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 289.000 | − | 500.563i | 0.0273956 | − | 0.0474505i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4570.00 | −0.427862 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12356.0 | 1.14970 | 0.574850 | − | 0.818259i | \(-0.305060\pi\) | ||||
0.574850 | + | 0.818259i | \(0.305060\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8370.00 | + | 14497.3i | −0.769313 | + | 1.33249i | 0.168623 | + | 0.985681i | \(0.446068\pi\) |
−0.937936 | + | 0.346809i | \(0.887265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4837.50 | + | 8378.80i | 0.441927 | + | 0.765440i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4884.00 | + | 8459.34i | 0.440799 | + | 0.763487i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7046.00 | − | 12204.0i | 0.632109 | − | 1.09484i | −0.355011 | − | 0.934862i | \(-0.615523\pi\) |
0.987120 | − | 0.159982i | \(-0.0511438\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2313.00 | −0.205033 | −0.102516 | − | 0.994731i | \(-0.532689\pi\) | ||||
−0.102516 | + | 0.994731i | \(0.532689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5775.00 | −0.508879 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7462.50 | + | 12925.4i | −0.649842 | + | 1.12556i | 0.333319 | + | 0.942814i | \(0.391832\pi\) |
−0.983160 | + | 0.182745i | \(0.941502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4378.00 | + | 7582.92i | 0.379005 | + | 0.656455i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1435.00 | − | 2485.49i | −0.122784 | − | 0.212668i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2740.50 | − | 4746.69i | 0.233128 | − | 0.403789i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5820.00 | 0.489403 | 0.244701 | − | 0.969598i | \(-0.421310\pi\) | ||||
0.244701 | + | 0.969598i | \(0.421310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20875.0 | −1.74532 | −0.872658 | − | 0.488332i | \(-0.837605\pi\) | ||||
−0.872658 | + | 0.488332i | \(0.837605\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7012.50 | + | 12146.0i | −0.579638 | + | 1.00396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10661.0 | − | 18465.4i | −0.876223 | − | 1.51766i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2244.00 | − | 3886.72i | −0.182361 | − | 0.315859i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 735.000 | − | 1273.06i | 0.0593959 | − | 0.102877i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1269.00 | −0.101409 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22442.0 | 1.78347 | 0.891735 | − | 0.452559i | \(-0.149489\pi\) | ||||
0.891735 | + | 0.452559i | \(0.149489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −850.000 | + | 1472.24i | −0.0668073 | + | 0.115714i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4307.50 | − | 7460.81i | −0.336701 | − | 0.583183i | 0.647109 | − | 0.762397i | \(-0.275978\pi\) |
−0.983810 | + | 0.179214i | \(0.942644\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 258.000 | + | 446.869i | 0.0199477 | + | 0.0345504i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3839.00 | + | 6649.34i | −0.295210 | + | 0.511318i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19524.0 | 1.48520 | 0.742602 | − | 0.669733i | \(-0.233592\pi\) | ||||
0.742602 | + | 0.669733i | \(0.233592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7531.00 | 0.569816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6507.00 | + | 11270.5i | −0.487100 | + | 0.843682i | −0.999890 | − | 0.0148320i | \(-0.995279\pi\) |
0.512790 | + | 0.858514i | \(0.328612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1702.50 | + | 2948.82i | 0.126769 | + | 0.219571i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9168.00 | + | 15879.4i | 0.675470 | + | 1.16995i | 0.976331 | + | 0.216281i | \(0.0693926\pi\) |
−0.300861 | + | 0.953668i | \(0.597274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1591.00 | + | 2755.69i | −0.116605 | + | 0.201965i | −0.918420 | − | 0.395607i | \(-0.870534\pi\) |
0.801815 | + | 0.597572i | \(0.203868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4575.00 | 0.331810 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7088.00 | 0.511399 | 0.255700 | − | 0.966756i | \(-0.417694\pi\) | ||||
0.255700 | + | 0.966756i | \(0.417694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11418.0 | − | 19776.6i | 0.815316 | − | 1.41217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1026.00 | − | 1777.08i | −0.0728861 | − | 0.126242i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3171.00 | − | 5492.33i | −0.222966 | − | 0.386189i | 0.732741 | − | 0.680508i | \(-0.238241\pi\) |
−0.955707 | + | 0.294319i | \(0.904907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −374.000 | + | 647.787i | −0.0261637 | + | 0.0453168i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26253.0 | 1.81801 | 0.909006 | − | 0.416782i | \(-0.136842\pi\) | ||||
0.909006 | + | 0.416782i | \(0.136842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8250.00 | −0.568432 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2691.00 | − | 4660.95i | 0.183558 | − | 0.317932i | −0.759532 | − | 0.650470i | \(-0.774572\pi\) |
0.943090 | + | 0.332538i | \(0.107905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14205.5 | + | 24604.6i | 0.964150 | + | 1.66996i | 0.711880 | + | 0.702301i | \(0.247844\pi\) |
0.252270 | + | 0.967657i | \(0.418823\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3125.00 | − | 5412.66i | −0.209999 | − | 0.363729i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7687.00 | + | 13314.3i | −0.514013 | + | 0.890296i | 0.485855 | + | 0.874039i | \(0.338508\pi\) |
−0.999868 | + | 0.0162568i | \(0.994825\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10353.0 | 0.685495 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23983.0 | −1.58020 | −0.790101 | − | 0.612976i | \(-0.789972\pi\) | ||||
−0.790101 | + | 0.612976i | \(0.789972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6886.50 | − | 11927.8i | 0.449336 | − | 0.778272i | −0.549007 | − | 0.835818i | \(-0.684994\pi\) |
0.998343 | + | 0.0575455i | \(0.0183274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5573.00 | + | 9652.72i | 0.361870 | + | 0.626778i | 0.988269 | − | 0.152725i | \(-0.0488050\pi\) |
−0.626398 | + | 0.779503i | \(0.715472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9372.00 | + | 16232.8i | 0.602699 | + | 1.04390i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2550.00 | 0.161646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2080.00 | −0.131226 | −0.0656129 | − | 0.997845i | \(-0.520900\pi\) | ||||
−0.0656129 | + | 0.997845i | \(0.520900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1445.00 | − | 2502.81i | 0.0903041 | − | 0.156411i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1198.50 | − | 2075.86i | −0.0745468 | − | 0.129119i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15525.0 | + | 26890.1i | 0.956631 | + | 1.65693i | 0.730590 | + | 0.682816i | \(0.239245\pi\) |
0.226041 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4541.50 | + | 7866.11i | −0.278537 | + | 0.482440i | −0.971021 | − | 0.238993i | \(-0.923183\pi\) |
0.692484 | + | 0.721433i | \(0.256516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4740.00 | −0.288020 | −0.144010 | − | 0.989576i | \(-0.546000\pi\) | ||||
−0.144010 | + | 0.989576i | \(0.546000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −540.000 | −0.0326608 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4098.00 | − | 7097.94i | 0.245585 | − | 0.425366i | −0.716711 | − | 0.697371i | \(-0.754353\pi\) |
0.962296 | + | 0.272004i | \(0.0876866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1957.50 | − | 3390.49i | −0.116772 | − | 0.202256i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3456.00 | − | 5985.97i | −0.204289 | − | 0.353839i | 0.745617 | − | 0.666375i | \(-0.232155\pi\) |
−0.949906 | + | 0.312536i | \(0.898822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14219.0 | − | 24628.0i | 0.836694 | − | 1.44920i | −0.0559490 | − | 0.998434i | \(-0.517818\pi\) |
0.892643 | − | 0.450764i | \(-0.148848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −440.000 | −0.0256578 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23607.0 | 1.37041 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2043.00 | + | 3538.58i | −0.117540 | + | 0.203585i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −973.000 | − | 1685.29i | −0.0557302 | − | 0.0965275i | 0.836814 | − | 0.547487i | \(-0.184415\pi\) |
−0.892545 | + | 0.450959i | \(0.851082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12978.0 | + | 22478.6i | 0.736758 | + | 1.27610i | 0.953948 | + | 0.299973i | \(0.0969776\pi\) |
−0.217190 | + | 0.976129i | \(0.569689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10054.0 | − | 17414.0i | 0.568243 | − | 0.984226i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8184.00 | −0.458495 | −0.229247 | − | 0.973368i | \(-0.573627\pi\) | ||||
−0.229247 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1170.00 | −0.0652604 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1938.00 | − | 3356.71i | 0.107158 | − | 0.185603i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15211.0 | − | 26346.2i | −0.837415 | − | 1.45045i | −0.892049 | − | 0.451939i | \(-0.850733\pi\) |
0.0546341 | − | 0.998506i | \(-0.482601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7925.00 | + | 13726.5i | 0.432536 | + | 0.749174i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9900.00 | − | 17147.3i | 0.538005 | − | 0.931851i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27273.0 | 1.46945 | 0.734727 | − | 0.678363i | \(-0.237310\pi\) | ||||
0.734727 | + | 0.678363i | \(0.237310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 136.000 | 0.00729635 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12705.0 | − | 22005.7i | 0.675843 | − | 1.17059i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14470.0 | − | 25062.8i | −0.766477 | − | 1.32758i | −0.939462 | − | 0.342653i | \(-0.888675\pi\) |
0.172985 | − | 0.984924i | \(-0.444659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17110.5 | + | 29636.3i | 0.898728 | + | 1.55664i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −382.500 | + | 662.509i | −0.0200066 | + | 0.0346524i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −606.000 | −0.0314325 | −0.0157163 | − | 0.999876i | \(-0.505003\pi\) | ||||
−0.0157163 | + | 0.999876i | \(0.505003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12628.0 | 0.652276 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1612.50 | + | 2792.93i | −0.0826024 | + | 0.143072i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6542.00 | + | 11331.1i | 0.333741 | + | 0.578056i | 0.983242 | − | 0.182305i | \(-0.0583557\pi\) |
−0.649502 | + | 0.760360i | \(0.725022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16612.5 | + | 28773.7i | 0.840541 | + | 1.45586i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13537.0 | + | 23446.8i | −0.682129 | + | 1.18148i | 0.292201 | + | 0.956357i | \(0.405612\pi\) |
−0.974330 | + | 0.225125i | \(0.927721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2196.00 | 0.109757 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3580.00 | −0.178204 | −0.0891018 | − | 0.996023i | \(-0.528400\pi\) | ||||
−0.0891018 | + | 0.996023i | \(0.528400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6973.50 | − | 12078.5i | 0.344324 | − | 0.596387i | −0.640907 | − | 0.767619i | \(-0.721441\pi\) |
0.985231 | + | 0.171232i | \(0.0547747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3157.50 | − | 5468.95i | −0.155278 | − | 0.268949i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3234.00 | + | 5601.45i | 0.157767 | + | 0.273261i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15636.5 | − | 27083.2i | 0.759766 | − | 1.31595i | −0.183204 | − | 0.983075i | \(-0.558647\pi\) |
0.942970 | − | 0.332878i | \(-0.108020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4255.00 | −0.205106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31729.0 | −1.52340 | −0.761698 | − | 0.647933i | \(-0.775634\pi\) | ||||
−0.761698 | + | 0.647933i | \(0.775634\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1569.00 | − | 2717.59i | 0.0747388 | − | 0.129451i | −0.826234 | − | 0.563327i | \(-0.809521\pi\) |
0.900973 | + | 0.433876i | \(0.142854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3740.00 | − | 6477.87i | −0.177454 | − | 0.307359i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −510.000 | − | 883.346i | −0.0240092 | − | 0.0415851i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10403.5 | + | 18019.4i | −0.487854 | + | 0.844988i | −0.999902 | − | 0.0139685i | \(-0.995554\pi\) |
0.512048 | + | 0.858957i | \(0.328887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33078.0 | 1.53911 | 0.769556 | − | 0.638580i | \(-0.220478\pi\) | ||||
0.769556 | + | 0.638580i | \(0.220478\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4675.00 | −0.216685 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 528.000 | − | 914.523i | 0.0242844 | − | 0.0420618i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1998.00 | + | 3460.64i | 0.0915417 | + | 0.158555i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5697.50 | + | 9868.36i | 0.259048 | + | 0.448684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6270.50 | − | 10860.8i | 0.284014 | − | 0.491927i | −0.688355 | − | 0.725374i | \(-0.741667\pi\) |
0.972370 | + | 0.233447i | \(0.0750004\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14982.0 | −0.673450 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7718.00 | −0.345617 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15990.0 | + | 27695.5i | −0.710659 | + | 1.23090i | 0.253952 | + | 0.967217i | \(0.418270\pi\) |
−0.964610 | + | 0.263680i | \(0.915064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22837.5 | + | 39555.7i | 1.01118 | + | 1.75141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1791.00 | + | 3102.10i | 0.0787086 | + | 0.136327i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10065.0 | + | 17433.1i | −0.440677 | + | 0.763274i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3792.00 | −0.164796 | −0.0823978 | − | 0.996600i | \(-0.526258\pi\) | ||||
−0.0823978 | + | 0.996600i | \(0.526258\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24086.0 | 1.04288 | 0.521439 | − | 0.853289i | \(-0.325395\pi\) | ||||
0.521439 | + | 0.853289i | \(0.325395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3242.50 | + | 5616.17i | −0.139362 | + | 0.241382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 886.000 | + | 1534.60i | 0.0379403 | + | 0.0657145i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4887.00 | − | 8464.53i | −0.207744 | − | 0.359822i | 0.743260 | − | 0.669003i | \(-0.233279\pi\) |
−0.951003 | + | 0.309180i | \(0.899945\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19318.0 | + | 33459.8i | −0.818206 | + | 1.41717i | 0.0887976 | + | 0.996050i | \(0.471698\pi\) |
−0.907003 | + | 0.421124i | \(0.861636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16458.0 | −0.692020 | −0.346010 | − | 0.938231i | \(-0.612464\pi\) | ||||
−0.346010 | + | 0.938231i | \(0.612464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20252.0 | 0.848469 | 0.424235 | − | 0.905552i | \(-0.360543\pi\) | ||||
0.424235 | + | 0.905552i | \(0.360543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5287.50 | − | 9158.22i | 0.219929 | − | 0.380929i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 810.000 | + | 1402.96i | 0.0335703 | + | 0.0581455i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20361.0 | + | 35266.3i | 0.837830 | + | 1.45116i | 0.891705 | + | 0.452617i | \(0.149510\pi\) |
−0.0538744 | + | 0.998548i | \(0.517157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3874.00 | − | 6709.96i | 0.158842 | − | 0.275123i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9540.00 | 0.388386 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27500.0 | 1.11560 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3111.00 | − | 5388.41i | 0.125316 | − | 0.217053i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6056.50 | − | 10490.2i | −0.243107 | − | 0.421074i | 0.718490 | − | 0.695537i | \(-0.244833\pi\) |
−0.961598 | + | 0.274463i | \(0.911500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 963.000 | + | 1667.96i | 0.0383844 | + | 0.0664838i | 0.884579 | − | 0.466390i | \(-0.154446\pi\) |
−0.846195 | + | 0.532873i | \(0.821112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2197.00 | + | 3805.32i | −0.0872650 | + | 0.151147i | −0.906354 | − | 0.422519i | \(-0.861146\pi\) |
0.819089 | + | 0.573666i | \(0.194479\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37491.0 | −1.47880 | −0.739402 | − | 0.673264i | \(-0.764892\pi\) | ||||
−0.739402 | + | 0.673264i | \(0.764892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 870.000 | 0.0341976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1570.50 | + | 2720.19i | −0.0613067 | + | 0.106186i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2074.00 | + | 3592.27i | 0.0806829 | + | 0.139747i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1375.00 | − | 2381.57i | −0.0531240 | − | 0.0920134i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10662.5 | − | 18468.0i | 0.410544 | − | 0.711083i | −0.584405 | − | 0.811462i | \(-0.698672\pi\) |
0.994949 | + | 0.100379i | \(0.0320055\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17982.0 | 0.687661 | 0.343830 | − | 0.939032i | \(-0.388276\pi\) | ||||
0.343830 | + | 0.939032i | \(0.388276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25636.0 | −0.977033 | −0.488516 | − | 0.872555i | \(-0.662462\pi\) | ||||
−0.488516 | + | 0.872555i | \(0.662462\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2110.50 | + | 3655.49i | −0.0798914 | + | 0.138376i | −0.903203 | − | 0.429214i | \(-0.858791\pi\) |
0.823312 | + | 0.567590i | \(0.192124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6358.00 | + | 11012.4i | 0.239866 | + | 0.415459i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1218.00 | + | 2109.64i | 0.0456426 | + | 0.0790553i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11490.0 | + | 19901.3i | −0.429127 | + | 0.743269i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24123.0 | −0.894936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17100.0 | 0.632279 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1370.00 | − | 2372.91i | 0.0503208 | − | 0.0871582i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14196.5 | + | 24589.1i | 0.519721 | + | 0.900183i | 0.999737 | + | 0.0229237i | \(0.00729748\pi\) |
−0.480016 | + | 0.877260i | \(0.659369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5028.00 | + | 8708.75i | 0.182860 | + | 0.316722i | 0.942853 | − | 0.333208i | \(-0.108131\pi\) |
−0.759994 | + | 0.649931i | \(0.774798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4671.00 | − | 8090.41i | 0.169318 | − | 0.293268i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17226.0 | 0.620341 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37249.0 | −1.33703 | −0.668515 | − | 0.743698i | \(-0.733070\pi\) | ||||
−0.668515 | + | 0.743698i | \(0.733070\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3774.00 | + | 6536.76i | −0.134586 | + | 0.233109i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 425.000 | + | 736.122i | 0.0151069 | + | 0.0261660i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 834.000 | + | 1444.53i | 0.0294539 | + | 0.0510156i | 0.880377 | − | 0.474275i | \(-0.157290\pi\) |
−0.850923 | + | 0.525291i | \(0.823957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 282.000 | − | 488.438i | 0.00992715 | − | 0.0171943i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3375.00 | −0.118047 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2786.00 | 0.0971341 | 0.0485671 | − | 0.998820i | \(-0.484535\pi\) | ||||
0.0485671 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4306.50 | + | 7459.08i | −0.149190 | + | 0.258405i | −0.930928 | − | 0.365202i | \(-0.881000\pi\) |
0.781738 | + | 0.623607i | \(0.214333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24156.0 | − | 41839.4i | −0.834176 | − | 1.44483i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27801.0 | + | 48152.7i | 0.953972 | + | 1.65233i | 0.736704 | + | 0.676215i | \(0.236381\pi\) |
0.217267 | + | 0.976112i | \(0.430286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3383.00 | + | 5859.53i | −0.115718 | + | 0.200430i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10785.0 | −0.366590 | −0.183295 | − | 0.983058i | \(-0.558676\pi\) | ||||
−0.183295 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23190.0 | −0.785770 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2574.00 | − | 4458.30i | 0.0866724 | − | 0.150121i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2589.00 | − | 4484.28i | −0.0869054 | − | 0.150525i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8605.00 | − | 14904.3i | −0.287052 | − | 0.497188i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17531.0 | − | 30364.6i | 0.582998 | − | 1.00978i | −0.412124 | − | 0.911128i | \(-0.635213\pi\) |
0.995122 | − | 0.0986541i | \(-0.0314538\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49701.0 | −1.64262 | −0.821308 | − | 0.570484i | \(-0.806755\pi\) | ||||
−0.821308 | + | 0.570484i | \(0.806755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69740.0 | −2.29780 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3955.50 | − | 6851.13i | 0.129527 | − | 0.224347i | −0.793967 | − | 0.607961i | \(-0.791988\pi\) |
0.923493 | + | 0.383614i | \(0.125321\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3834.00 | + | 6640.68i | 0.125164 | + | 0.216790i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18859.5 | − | 32665.6i | −0.611927 | − | 1.05989i | −0.990915 | − | 0.134488i | \(-0.957061\pi\) |
0.378988 | − | 0.925402i | \(-0.376272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8280.00 | + | 14341.4i | −0.267840 | + | 0.463913i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 81069.0 | 2.60652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54725.0 | 1.75418 | 0.877092 | − | 0.480322i | \(-0.159480\pi\) | ||||
0.877092 | + | 0.480322i | \(0.159480\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4362.50 | − | 7556.07i | 0.138996 | − | 0.240747i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3252.50 | + | 5633.50i | 0.103318 | + | 0.178951i | 0.913050 | − | 0.407848i | \(-0.133721\pi\) |
−0.809732 | + | 0.586800i | \(0.800388\pi\) | |||||||
\(998\) | 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 | 1620.4.i.k.1081.1 | 2 | ||
3.2 | odd | 2 | 1620.4.i.e.1081.1 | 2 | |||
9.2 | odd | 6 | 1620.4.i.e.541.1 | 2 | |||
9.4 | even | 3 | 540.4.a.a.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 540.4.a.c.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 1620.4.i.k.541.1 | 2 | ||
36.23 | even | 6 | 2160.4.a.s.1.1 | 1 | |||
36.31 | odd | 6 | 2160.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.4.a.a.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
540.4.a.c.1.1 | yes | 1 | 9.5 | odd | 6 | ||
1620.4.i.e.541.1 | 2 | 9.2 | odd | 6 | |||
1620.4.i.e.1081.1 | 2 | 3.2 | odd | 2 | |||
1620.4.i.k.541.1 | 2 | 9.7 | even | 3 | inner | ||
1620.4.i.k.1081.1 | 2 | 1.1 | even | 1 | trivial | ||
2160.4.a.h.1.1 | 1 | 36.31 | odd | 6 | |||
2160.4.a.s.1.1 | 1 | 36.23 | even | 6 |