Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(49,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.ba (of order \(6\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(1.40994 + 0.109843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.49 |
Dual form | 1300.2.ba.c.849.3 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.01978 | − | 1.16612i | 1.16612 | − | 0.673262i | 0.213359 | − | 0.976974i | \(-0.431559\pi\) |
0.952764 | + | 0.303712i | \(0.0982261\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.199902 | + | 0.346241i | −0.0755559 | + | 0.130867i | −0.901328 | − | 0.433137i | \(-0.857406\pi\) |
0.825772 | + | 0.564004i | \(0.190740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.21969 | − | 2.11256i | 0.406562 | − | 0.704187i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.452267 | − | 0.261116i | −0.256520 | − | 0.966539i | \(-0.582576\pi\) |
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55193 | + | 0.619491i | 0.985129 | + | 0.171816i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.599706 | + | 0.346241i | 0.145450 | + | 0.0839757i | 0.570959 | − | 0.820979i | \(-0.306572\pi\) |
−0.425509 | + | 0.904954i | \(0.639905\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.65213 | + | 2.68591i | 1.06727 | + | 0.616190i | 0.927435 | − | 0.373985i | \(-0.122009\pi\) |
0.139837 | + | 0.990175i | \(0.455342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.932442i | 0.203476i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0927749 | + | 0.0535636i | −0.0193449 | + | 0.0111688i | −0.509641 | − | 0.860387i | \(-0.670222\pi\) |
0.490296 | + | 0.871556i | \(0.336889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.30752i | 0.251632i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.45174 | − | 4.24653i | −0.455276 | − | 0.788562i | 0.543428 | − | 0.839456i | \(-0.317126\pi\) |
−0.998704 | + | 0.0508943i | \(0.983793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.86488i | − | 1.41257i | −0.707925 | − | 0.706287i | \(-0.750369\pi\) | ||
0.707925 | − | 0.706287i | \(-0.249631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.01978 | − | 3.49837i | 0.351599 | − | 0.608988i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.13234 | + | 1.96128i | 0.186156 | + | 0.322432i | 0.943966 | − | 0.330044i | \(-0.107064\pi\) |
−0.757809 | + | 0.652476i | \(0.773730\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.89654 | − | 2.89075i | 1.26446 | − | 0.462891i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.69615 | − | 3.86603i | 1.04576 | − | 0.603772i | 0.124303 | − | 0.992244i | \(-0.460331\pi\) |
0.921460 | + | 0.388473i | \(0.126997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.20533 | − | 3.00530i | −0.793806 | − | 0.458304i | 0.0474947 | − | 0.998871i | \(-0.484876\pi\) |
−0.841301 | + | 0.540567i | \(0.818210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.42008 | + | 5.92375i | 0.488583 | + | 0.846250i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.61504 | 0.226150 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.7189i | − | 1.60972i | −0.593468 | − | 0.804858i | \(-0.702242\pi\) | ||
0.593468 | − | 0.804858i | \(-0.297758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.5284 | 1.65943 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.30059 | + | 3.63765i | 0.820267 | + | 0.473581i | 0.850508 | − | 0.525961i | \(-0.176294\pi\) |
−0.0302418 | + | 0.999543i | \(0.509628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.34461 | + | 7.52509i | −0.556270 | + | 0.963489i | 0.441533 | + | 0.897245i | \(0.354435\pi\) |
−0.997803 | + | 0.0662436i | \(0.978899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.487636 | + | 0.844610i | 0.0614364 | + | 0.106411i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.664004 | − | 1.15009i | −0.0811210 | − | 0.140506i | 0.822611 | − | 0.568605i | \(-0.192517\pi\) |
−0.903732 | + | 0.428099i | \(0.859183\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.124924 | + | 0.216374i | −0.0150390 | + | 0.0260484i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.35847 | − | 1.93902i | −0.398577 | − | 0.230119i | 0.287293 | − | 0.957843i | \(-0.407245\pi\) |
−0.685870 | + | 0.727724i | \(0.740578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2251 | −1.19676 | −0.598380 | − | 0.801213i | \(-0.704189\pi\) | ||||
−0.598380 | + | 0.801213i | \(0.704189\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.692481i | 0.0789156i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1533 | 1.47986 | 0.739932 | − | 0.672681i | \(-0.234858\pi\) | ||||
0.739932 | + | 0.672681i | \(0.234858\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.18379 | + | 8.97859i | 0.575976 | + | 0.997621i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0791 | −1.54539 | −0.772693 | − | 0.634780i | \(-0.781091\pi\) | ||||
−0.772693 | + | 0.634780i | \(0.781091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.90396 | − | 5.71806i | −1.06182 | − | 0.613040i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.300587 | + | 0.173544i | −0.0318622 | + | 0.0183956i | −0.515846 | − | 0.856681i | \(-0.672523\pi\) |
0.483984 | + | 0.875077i | \(0.339189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.924532 | + | 1.10599i | −0.0969173 | + | 0.115939i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.17142 | − | 15.8854i | −0.951032 | − | 1.64724i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.42502 | − | 7.66436i | 0.449293 | − | 0.778198i | −0.549047 | − | 0.835791i | \(-0.685009\pi\) |
0.998340 | + | 0.0575932i | \(0.0183426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.22512i | − | 0.424640i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.05193 | + | 3.55405i | 0.204175 | + | 0.353641i | 0.949870 | − | 0.312646i | \(-0.101216\pi\) |
−0.745695 | + | 0.666288i | \(0.767882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2325i | 1.10677i | 0.832926 | + | 0.553384i | \(0.186664\pi\) | ||||
−0.832926 | + | 0.553384i | \(0.813336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.2449 | + | 8.80165i | −1.47378 | + | 0.850888i | −0.999564 | − | 0.0295208i | \(-0.990602\pi\) |
−0.474216 | + | 0.880408i | \(0.657269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.1830i | − | 1.45427i | −0.686495 | − | 0.727134i | \(-0.740852\pi\) | ||
0.686495 | − | 0.727134i | \(-0.259148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.57418 | + | 2.64091i | 0.434162 | + | 0.250664i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.70781 | + | 4.45011i | 0.725090 | + | 0.418631i | 0.816623 | − | 0.577171i | \(-0.195843\pi\) |
−0.0915332 | + | 0.995802i | \(0.529177\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.64096 | − | 6.74809i | 0.521507 | − | 0.623861i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.239765 | + | 0.138429i | −0.0219792 | + | 0.0126897i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.01652 | − | 15.6171i | 0.812993 | − | 1.40814i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5279 | + | 6.07829i | −0.934201 | + | 0.539361i | −0.888138 | − | 0.459577i | \(-0.848001\pi\) |
−0.0460632 | + | 0.998939i | \(0.514668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.0182 | −1.23423 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.11773 | −0.185027 | −0.0925135 | − | 0.995711i | \(-0.529490\pi\) | ||||
−0.0925135 | + | 0.995711i | \(0.529490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.85994 | + | 1.07384i | −0.161277 | + | 0.0931135i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.01652 | + | 15.6171i | −0.770334 | + | 1.33426i | 0.167046 | + | 0.985949i | \(0.446577\pi\) |
−0.937380 | + | 0.348308i | \(0.886756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.92008 | + | 8.52183i | −0.417316 | + | 0.722812i | −0.995668 | − | 0.0929749i | \(-0.970362\pi\) |
0.578353 | + | 0.815787i | \(0.303696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.99674 | + | 4.03957i | −0.589232 | + | 0.340193i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.86440 | − | 2.14683i | 0.490405 | − | 0.179527i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.8156 | + | 7.97647i | 1.13950 | + | 0.657888i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.69289 | + | 4.44149i | 0.630226 | + | 0.363861i | 0.780840 | − | 0.624731i | \(-0.214792\pi\) |
−0.150613 | + | 0.988593i | \(0.548125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.43937i | − | 0.361271i | −0.983550 | − | 0.180636i | \(-0.942185\pi\) | ||
0.983550 | − | 0.180636i | \(-0.0578155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.46291 | − | 0.844610i | 0.118269 | − | 0.0682827i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.16719i | − | 0.332578i | −0.986077 | − | 0.166289i | \(-0.946822\pi\) | ||
0.986077 | − | 0.166289i | \(-0.0531784\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.6657 | − | 23.6697i | −1.08376 | − | 1.87713i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.0428299i | − | 0.00337547i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.84836 | − | 3.20145i | 0.144775 | − | 0.250757i | −0.784514 | − | 0.620111i | \(-0.787088\pi\) |
0.929289 | + | 0.369354i | \(0.120421\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7486 | − | 18.6171i | −0.831750 | − | 1.44063i | −0.896650 | − | 0.442741i | \(-0.854006\pi\) |
0.0648999 | − | 0.997892i | \(-0.479327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2325 | + | 4.40078i | 0.940959 | + | 0.338522i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3483 | − | 6.55193i | 0.867825 | − | 0.501039i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0561 | + | 5.80589i | 0.764551 | + | 0.441414i | 0.830927 | − | 0.556381i | \(-0.187811\pi\) |
−0.0663766 | + | 0.997795i | \(0.521144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9678 | 1.27538 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.48516 | + | 4.30442i | 0.185749 | + | 0.321728i | 0.943829 | − | 0.330435i | \(-0.107195\pi\) |
−0.758079 | + | 0.652162i | \(0.773862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3695 | −1.29107 | −0.645534 | − | 0.763732i | \(-0.723365\pi\) | ||||
−0.645534 | + | 0.763732i | \(0.723365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.2654i | 1.49806i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.19941 | 0.0877098 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.452716 | − | 0.261376i | −0.0329303 | − | 0.0190123i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2523 | − | 17.7575i | 0.741832 | − | 1.28489i | −0.209828 | − | 0.977738i | \(-0.567290\pi\) |
0.951660 | − | 0.307153i | \(-0.0993762\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3038 | + | 23.0428i | 0.957626 | + | 1.65866i | 0.728240 | + | 0.685322i | \(0.240338\pi\) |
0.229386 | + | 0.973336i | \(0.426328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.204141 | + | 0.353583i | 0.0145445 | + | 0.0251917i | 0.873206 | − | 0.487351i | \(-0.162037\pi\) |
−0.858662 | + | 0.512543i | \(0.828704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1998 | + | 21.1307i | −0.864823 | + | 1.49792i | 0.00240070 | + | 0.999997i | \(0.499236\pi\) |
−0.867223 | + | 0.497919i | \(0.834098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.68229 | − | 1.54862i | −0.189194 | − | 0.109231i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.96043 | 0.137595 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.261323i | 0.0181632i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.30426 | 0.643589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.880509 | − | 1.52509i | −0.0606167 | − | 0.104991i | 0.834125 | − | 0.551576i | \(-0.185973\pi\) |
−0.894741 | + | 0.446585i | \(0.852640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.04452 | −0.619721 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.72314 | + | 1.57221i | 0.184859 | + | 0.106728i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.6525 | + | 11.9237i | −1.39557 | + | 0.805732i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.91562 | + | 1.60134i | 0.128859 | + | 0.107718i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.65955 | − | 9.80263i | −0.378991 | − | 0.656433i | 0.611924 | − | 0.790916i | \(-0.290396\pi\) |
−0.990916 | + | 0.134484i | \(0.957062\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.03039 | − | 6.98084i | 0.267506 | − | 0.463334i | −0.700711 | − | 0.713445i | \(-0.747134\pi\) |
0.968217 | + | 0.250111i | \(0.0804671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5715i | 0.764666i | 0.924025 | + | 0.382333i | \(0.124879\pi\) | ||||
−0.924025 | + | 0.382333i | \(0.875121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.807519 | + | 1.39866i | 0.0531308 | + | 0.0920253i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0900i | 1.57819i | 0.614272 | + | 0.789094i | \(0.289450\pi\) | ||||
−0.614272 | + | 0.789094i | \(0.710550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.5669 | − | 15.3384i | 1.72570 | − | 0.996336i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.7089i | − | 1.98639i | −0.116459 | − | 0.993196i | \(-0.537154\pi\) | ||
0.116459 | − | 0.993196i | \(-0.462846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.86541 | + | 3.96374i | 0.442240 | + | 0.255327i | 0.704547 | − | 0.709657i | \(-0.251150\pi\) |
−0.262308 | + | 0.964984i | \(0.584483\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.5432 | + | 10.1286i | 1.12540 | + | 0.649750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.8602 | + | 12.4221i | 0.945529 | + | 0.790401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.4368 | + | 16.4180i | −1.80211 | + | 1.04045i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.3112 | − | 19.5916i | 0.713956 | − | 1.23661i | −0.249405 | − | 0.968399i | \(-0.580235\pi\) |
0.963361 | − | 0.268209i | \(-0.0864317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0927749 | + | 0.160691i | −0.00583271 | + | 0.0101025i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.3403 | + | 12.8982i | −1.39355 | + | 0.804566i | −0.993706 | − | 0.112018i | \(-0.964269\pi\) |
−0.399843 | + | 0.916584i | \(0.630935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.905432 | −0.0562608 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.9614 | −0.740393 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.37748 | + | 0.795286i | −0.0849388 | + | 0.0490394i | −0.541868 | − | 0.840464i | \(-0.682283\pi\) |
0.456929 | + | 0.889503i | \(0.348949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.404747 | + | 0.701043i | −0.0247701 | + | 0.0429031i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.9114 | + | 24.0952i | −0.848192 | + | 1.46911i | 0.0346278 | + | 0.999400i | \(0.488975\pi\) |
−0.882820 | + | 0.469712i | \(0.844358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3520 | + | 11.7502i | −1.23629 | + | 0.713774i | −0.968335 | − | 0.249656i | \(-0.919682\pi\) |
−0.267959 | + | 0.963430i | \(0.586349\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.577640 | + | 3.31197i | −0.0349603 | + | 0.200450i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.59525 | − | 1.49837i | −0.155934 | − | 0.0900283i | 0.420003 | − | 0.907523i | \(-0.362029\pi\) |
−0.575936 | + | 0.817494i | \(0.695362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.6150 | − | 9.59270i | −0.994716 | − | 0.574300i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.6085i | − | 1.46802i | −0.679138 | − | 0.734011i | \(-0.737646\pi\) | ||
0.679138 | − | 0.734011i | \(-0.262354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.07446 | − | 4.08444i | 0.420533 | − | 0.242795i | −0.274772 | − | 0.961509i | \(-0.588603\pi\) |
0.695305 | + | 0.718715i | \(0.255269\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.09131i | 0.182474i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.26023 | − | 14.3071i | −0.485896 | − | 0.841597i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 20.6405i | − | 1.20997i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.75184 | + | 6.49837i | −0.219185 | + | 0.379639i | −0.954559 | − | 0.298022i | \(-0.903673\pi\) |
0.735374 | + | 0.677661i | \(0.237006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.13234 | + | 1.96128i | 0.0657053 | + | 0.113805i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.362712 | + | 0.132781i | −0.0209762 | + | 0.00767893i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08112 | − | 1.20153i | 0.119953 | − | 0.0692552i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.28893 | + | 4.78561i | 0.476186 | + | 0.274926i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.95293 | 0.339752 | 0.169876 | − | 0.985465i | \(-0.445663\pi\) | ||||
0.169876 | + | 0.985465i | \(0.445663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0984 | + | 22.6872i | 0.745144 | + | 1.29063i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9247 | −1.01642 | −0.508208 | − | 0.861235i | \(-0.669692\pi\) | ||||
−0.508208 | + | 0.861235i | \(0.669692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0073i | 0.961312i | 0.876909 | + | 0.480656i | \(0.159601\pi\) | ||||
−0.876909 | + | 0.480656i | \(0.840399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.09300 | 0.173720 | 0.0868601 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868601 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.35521 | − | 4.24653i | −0.411813 | − | 0.237760i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.5276 | + | 35.5549i | −1.14574 | + | 1.98448i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.85994 | + | 3.22151i | 0.103490 | + | 0.179250i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.7053 | − | 30.6664i | −0.979103 | − | 1.69586i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.692481 | − | 1.19941i | 0.0381777 | − | 0.0661258i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5481 | + | 11.2861i | 1.07446 | + | 0.620340i | 0.929397 | − | 0.369082i | \(-0.120328\pi\) |
0.145064 | + | 0.989422i | \(0.453661\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.52442 | 0.302736 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0603i | 0.983808i | 0.870649 | + | 0.491904i | \(0.163699\pi\) | ||||
−0.870649 | + | 0.491904i | \(0.836301\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.7575 | 1.12739 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.81119 | − | 11.7973i | −0.368847 | − | 0.638861i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.53335 | −0.298773 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.9252 | − | 13.2359i | −1.23069 | − | 0.710538i | −0.263514 | − | 0.964655i | \(-0.584882\pi\) |
−0.967173 | + | 0.254118i | \(0.918215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7190 | + | 6.18860i | −0.573773 | + | 0.331268i | −0.758655 | − | 0.651493i | \(-0.774143\pi\) |
0.184882 | + | 0.982761i | \(0.440810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.809996 | + | 4.64422i | −0.0432344 | + | 0.247890i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.64047 | − | 16.6978i | −0.513110 | − | 0.888733i | −0.999884 | − | 0.0152053i | \(-0.995160\pi\) |
0.486774 | − | 0.873528i | \(-0.338174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.322849 | + | 0.559192i | −0.0170870 | + | 0.0295956i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.5506i | − | 1.40129i | −0.713512 | − | 0.700643i | \(-0.752897\pi\) | ||
0.713512 | − | 0.700643i | \(-0.247103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.92820 | + | 8.53590i | 0.259379 | + | 0.449258i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.6580i | 0.979290i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.38638 | − | 3.68718i | 0.333366 | − | 0.192469i | −0.323968 | − | 0.946068i | \(-0.605017\pi\) |
0.657335 | + | 0.753599i | \(0.271684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 18.8614i | − | 0.981883i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.05756 | + | 2.34263i | 0.210658 | + | 0.121624i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.5214 | − | 14.1574i | −1.26967 | − | 0.733044i | −0.294744 | − | 0.955576i | \(-0.595234\pi\) |
−0.974925 | + | 0.222532i | \(0.928568\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.07772 | − | 16.6022i | −0.313018 | − | 0.855059i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.02975 | + | 5.21333i | −0.463827 | + | 0.267791i | −0.713652 | − | 0.700500i | \(-0.752960\pi\) |
0.249825 | + | 0.968291i | \(0.419627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1761 | + | 24.5537i | −0.726262 | + | 1.25792i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.42600 | + | 9.39811i | −0.277256 | + | 0.480221i | −0.970702 | − | 0.240288i | \(-0.922758\pi\) |
0.693446 | + | 0.720509i | \(0.256092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.6978 | + | 7.33105i | −0.645463 | + | 0.372658i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2893 | −1.02871 | −0.514353 | − | 0.857578i | \(-0.671968\pi\) | ||||
−0.514353 | + | 0.857578i | \(0.671968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0741836 | −0.00375163 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.27736 | + | 2.46953i | −0.215764 | + | 0.124572i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6263 | + | 21.8695i | −0.633698 | + | 1.09760i | 0.353091 | + | 0.935589i | \(0.385130\pi\) |
−0.986789 | + | 0.162008i | \(0.948203\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.50445 | + | 4.33784i | −0.125380 | + | 0.217164i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8377 | − | 6.25714i | 0.541208 | − | 0.312467i | −0.204360 | − | 0.978896i | \(-0.565511\pi\) |
0.745568 | + | 0.666429i | \(0.232178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.87223 | − | 27.9355i | 0.242703 | − | 1.39157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.39703 | + | 1.96128i | 0.168385 | + | 0.0972169i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.19248 | − | 2.99788i | −0.256752 | − | 0.148236i | 0.366100 | − | 0.930575i | \(-0.380693\pi\) |
−0.622852 | + | 0.782340i | \(0.714026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 42.0575i | 2.07454i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.51900 | + | 1.45435i | −0.123952 | + | 0.0715637i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.9497i | 1.12385i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.48516 | − | 9.50057i | −0.267968 | − | 0.464133i | 0.700369 | − | 0.713781i | \(-0.253019\pi\) |
−0.968337 | + | 0.249647i | \(0.919685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6085i | 1.78419i | 0.451848 | + | 0.892095i | \(0.350765\pi\) | ||||
−0.451848 | + | 0.892095i | \(0.649235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.22512 | + | 7.31812i | −0.205432 | + | 0.355819i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73699 | − | 3.00856i | −0.0840590 | − | 0.145595i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.34135 | − | 11.1747i | 0.451005 | − | 0.539521i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4873 | + | 6.05484i | −0.505155 | + | 0.291651i | −0.730840 | − | 0.682549i | \(-0.760871\pi\) |
0.225685 | + | 0.974200i | \(0.427538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.80977 | + | 4.50897i | 0.375314 | + | 0.216687i | 0.675777 | − | 0.737106i | \(-0.263808\pi\) |
−0.300464 | + | 0.953793i | \(0.597141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.575468 | −0.0275284 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.07547 | + | 10.5230i | 0.289966 | + | 0.502236i | 0.973801 | − | 0.227400i | \(-0.0730226\pi\) |
−0.683835 | + | 0.729637i | \(0.739689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.6857 | 0.794557 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.3116i | − | 0.727476i | −0.931501 | − | 0.363738i | \(-0.881500\pi\) | ||
0.931501 | − | 0.363738i | \(-0.118500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.7173 | 0.979895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6929 | + | 11.3697i | 0.929365 | + | 0.536569i | 0.886611 | − | 0.462516i | \(-0.153053\pi\) |
0.0427543 | + | 0.999086i | \(0.486387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.69615 | − | 11.5981i | 0.315310 | − | 0.546132i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.17686 | − | 8.96658i | −0.243230 | − | 0.421287i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.37252 | − | 9.30548i | −0.251316 | − | 0.435292i | 0.712572 | − | 0.701599i | \(-0.247530\pi\) |
−0.963888 | + | 0.266307i | \(0.914197\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.452716 | + | 0.784127i | −0.0211310 | + | 0.0365999i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.2973 | + | 5.94516i | 0.479594 | + | 0.276894i | 0.720247 | − | 0.693717i | \(-0.244028\pi\) |
−0.240653 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.39726 | −0.157884 | −0.0789420 | − | 0.996879i | \(-0.525154\pi\) | ||||
−0.0789420 | + | 0.996879i | \(0.525154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.39426i | − | 0.295891i | −0.988996 | − | 0.147946i | \(-0.952734\pi\) | ||
0.988996 | − | 0.147946i | \(-0.0472660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.530943 | 0.0245167 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.85945 | − | 8.41682i | −0.223912 | − | 0.387826i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.4107 | −0.478683 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.7569 | − | 14.2934i | −1.13354 | − | 0.654450i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.1330 | + | 8.15968i | −0.645752 | + | 0.372825i | −0.786827 | − | 0.617174i | \(-0.788278\pi\) |
0.141075 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.80702 | + | 7.66781i | 0.127989 | + | 0.349622i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0499450 | − | 0.0865072i | −0.00227258 | − | 0.00393622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.96728 | − | 10.3356i | 0.270403 | − | 0.468352i | −0.698562 | − | 0.715550i | \(-0.746176\pi\) |
0.968965 | + | 0.247197i | \(0.0795096\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.62166i | − | 0.389885i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0259 | − | 29.4896i | −0.768366 | − | 1.33085i | −0.938448 | − | 0.345419i | \(-0.887737\pi\) |
0.170082 | − | 0.985430i | \(-0.445597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.39557i | − | 0.152929i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.34273 | − | 0.775227i | 0.0602298 | − | 0.0347737i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12.5854i | − | 0.563398i | −0.959503 | − | 0.281699i | \(-0.909102\pi\) | ||
0.959503 | − | 0.281699i | \(-0.0908979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.4196 | − | 25.0683i | −1.93985 | − | 1.11997i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.7518 | − | 9.09433i | −0.702340 | − | 0.405496i | 0.105879 | − | 0.994379i | \(-0.466235\pi\) |
−0.808218 | + | 0.588883i | \(0.799568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.8388 | − | 5.37592i | 1.32519 | − | 0.238753i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.1265 | − | 14.5068i | 1.11371 | − | 0.643001i | 0.173923 | − | 0.984759i | \(-0.444356\pi\) |
0.939788 | + | 0.341758i | \(0.111022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.04402 | − | 3.54035i | 0.0904223 | − | 0.156616i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.51187 | + | 6.08275i | −0.155053 | + | 0.268560i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.19615 | + | 3.00000i | −0.228527 | + | 0.131940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0815 | 1.18875 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.0240 | 1.53443 | 0.767214 | − | 0.641391i | \(-0.221642\pi\) | ||||
0.767214 | + | 0.641391i | \(0.221642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.03447 | − | 4.63870i | 0.351323 | − | 0.202836i | −0.313945 | − | 0.949441i | \(-0.601651\pi\) |
0.665268 | + | 0.746605i | \(0.268317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.72314 | − | 4.71662i | 0.118622 | − | 0.205459i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4943 | + | 19.9086i | −0.499751 | + | 0.865593i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.3695 | − | 8.87358i | 0.666979 | − | 0.385080i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.1793 | − | 9.58366i | 1.13395 | − | 0.415114i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0390 | + | 5.79600i | 0.433214 | + | 0.250116i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.2602 | + | 5.92375i | 0.441940 | + | 0.255154i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.3814i | − | 1.04824i | −0.851644 | − | 0.524120i | \(-0.824394\pi\) | ||
0.851644 | − | 0.524120i | \(-0.175606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.0827 | + | 20.2550i | −1.50554 | + | 0.869226i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.5270i | 1.13421i | 0.823645 | + | 0.567106i | \(0.191937\pi\) | ||||
−0.823645 | + | 0.567106i | \(0.808063\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5981 | + | 18.3565i | 0.452317 | + | 0.783436i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 26.3406i | − | 1.12215i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.62938 | + | 4.55422i | −0.111813 | + | 0.193665i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.60586 | − | 2.78142i | −0.0680423 | − | 0.117853i | 0.829997 | − | 0.557768i | \(-0.188342\pi\) |
−0.898039 | + | 0.439915i | \(0.855009\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.6272 | − | 13.8993i | −0.703257 | − | 0.587877i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.42256 | − | 1.39866i | 0.102280 | − | 0.0590516i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.6918 | + | 17.1426i | 1.25136 | + | 0.722474i | 0.971380 | − | 0.237531i | \(-0.0763382\pi\) |
0.279982 | + | 0.960005i | \(0.409672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.14500 | −0.174074 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.8228 | + | 30.8701i | 0.747172 | + | 1.29414i | 0.949173 | + | 0.314755i | \(0.101922\pi\) |
−0.202001 | + | 0.979385i | \(0.564744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.53590 | −0.189821 | −0.0949107 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949107 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 47.8219i | − | 1.99779i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4475 | 0.767981 | 0.383991 | − | 0.923337i | \(-0.374550\pi\) | ||||
0.383991 | + | 0.923337i | \(0.374550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 53.7415 | + | 31.0277i | 2.23342 | + | 1.28947i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.81445 | − | 4.87477i | 0.116763 | − | 0.202240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1489 | − | 17.5784i | −0.420323 | − | 0.728021i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.4957 | − | 37.2316i | −0.887222 | − | 1.53671i | −0.843146 | − | 0.537685i | \(-0.819299\pi\) |
−0.0440760 | − | 0.999028i | \(-0.514034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.1244 | − | 36.5885i | 0.870414 | − | 1.50760i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.824642 | + | 0.476107i | 0.0339212 | + | 0.0195844i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.8614 | 0.528153 | 0.264076 | − | 0.964502i | \(-0.414933\pi\) | ||||
0.264076 | + | 0.964502i | \(0.414933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 56.9060i | 2.32901i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3170 | −1.15700 | −0.578500 | − | 0.815682i | \(-0.696362\pi\) | ||||
−0.578500 | + | 0.815682i | \(0.696362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.56734 | + | 6.17882i | 0.145515 | + | 0.252039i | 0.929565 | − | 0.368658i | \(-0.120183\pi\) |
−0.784050 | + | 0.620698i | \(0.786849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.23951 | −0.131923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2086 | + | 11.0901i | 0.779653 | + | 0.450133i | 0.836307 | − | 0.548261i | \(-0.184710\pi\) |
−0.0566544 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.95965 | − | 2.28610i | 0.160453 | − | 0.0926376i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3043 | − | 2.14598i | −0.497777 | − | 0.0868171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.161311 | + | 0.279399i | 0.00651530 | + | 0.0112848i | 0.869265 | − | 0.494347i | \(-0.164593\pi\) |
−0.862749 | + | 0.505632i | \(0.831259\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.5993 | − | 32.2150i | 0.748781 | − | 1.29693i | −0.199626 | − | 0.979872i | \(-0.563973\pi\) |
0.948407 | − | 0.317055i | \(-0.102694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.94911i | − | 0.158728i | −0.996846 | − | 0.0793641i | \(-0.974711\pi\) | ||
0.996846 | − | 0.0793641i | \(-0.0252890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0700354 | − | 0.121305i | −0.00281043 | − | 0.00486780i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.138767i | − | 0.00555959i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7926 | − | 10.8499i | 0.750504 | − | 0.433304i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.56825i | 0.0625304i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0824 | + | 16.7908i | 1.15775 | + | 0.668429i | 0.950765 | − | 0.309914i | \(-0.100300\pi\) |
0.206989 | + | 0.978343i | \(0.433634\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.55688 | − | 2.05356i | −0.141373 | − | 0.0816218i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.47818 | + | 23.1595i | 0.335918 | + | 0.917612i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.19257 | + | 4.72998i | −0.324093 | + | 0.187115i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5900 | − | 28.7347i | 0.655266 | − | 1.13495i | −0.326561 | − | 0.945176i | \(-0.605890\pi\) |
0.981827 | − | 0.189778i | \(-0.0607767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6833 | − | 27.1643i | 0.618489 | − | 1.07125i | −0.371273 | − | 0.928524i | \(-0.621078\pi\) |
0.989762 | − | 0.142730i | \(-0.0455882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9659 | + | 9.79529i | −0.667000 | + | 0.385092i | −0.794939 | − | 0.606690i | \(-0.792497\pi\) |
0.127939 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6012 | 0.494639 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.33355 | 0.287424 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.15962 | + | 3.55626i | −0.241044 | + | 0.139167i | −0.615657 | − | 0.788015i | \(-0.711109\pi\) |
0.374612 | + | 0.927182i | \(0.377776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4714 | + | 21.6012i | −0.486557 | + | 0.842742i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.29211 | − | 16.0944i | 0.361969 | − | 0.626949i | −0.626316 | − | 0.779570i | \(-0.715438\pi\) |
0.988285 | + | 0.152621i | \(0.0487712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5413 | − | 8.39540i | 0.565590 | − | 0.326543i | −0.189796 | − | 0.981823i | \(-0.560783\pi\) |
0.755386 | + | 0.655280i | \(0.227449\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.73650 | + | 1.00050i | 0.222787 | + | 0.0388563i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.454919 | + | 0.262648i | 0.0176146 | + | 0.0101698i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8621 | − | 13.1995i | −0.883902 | − | 0.510321i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0502i | 0.581005i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5647 | − | 11.2957i | 0.754165 | − | 0.435417i | −0.0730322 | − | 0.997330i | \(-0.523268\pi\) |
0.827197 | + | 0.561912i | \(0.189934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.31616i | 0.204317i | 0.994768 | + | 0.102158i | \(0.0325749\pi\) | ||||
−0.994768 | + | 0.102158i | \(0.967425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76914 | + | 3.06424i | 0.0678935 | + | 0.117595i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 18.7997i | − | 0.720407i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.97695 | − | 3.42419i | 0.0756461 | − | 0.131023i | −0.825721 | − | 0.564079i | \(-0.809231\pi\) |
0.901367 | + | 0.433056i | \(0.142565\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.4938 | + | 23.3719i | 0.514820 | + | 0.891694i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.25976 | − | 41.6248i | 0.276575 | − | 1.58578i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1493 | + | 6.43704i | −0.424139 | + | 0.244877i | −0.696846 | − | 0.717220i | \(-0.745414\pi\) |
0.272708 | + | 0.962097i | \(0.412081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.46291 | + | 0.844610i | 0.0555713 | + | 0.0320841i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.35430 | 0.202809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.0919 | + | 48.6566i | 1.06253 | + | 1.84036i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9777 | 1.32109 | 0.660544 | − | 0.750787i | \(-0.270326\pi\) | ||||
0.660544 | + | 0.750787i | \(0.270326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1655i | 0.458830i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.64074 | −0.0617065 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.1183 | + | 9.88325i | 0.642891 | + | 0.371173i | 0.785727 | − | 0.618573i | \(-0.212289\pi\) |
−0.142836 | + | 0.989746i | \(0.545622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.0429 | − | 27.7872i | 0.601657 | − | 1.04210i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.421272 | + | 0.729664i | 0.0157767 | + | 0.0273261i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.8103 | − | 62.0253i | −1.33736 | − | 2.31638i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.1234 | − | 38.3188i | 0.825062 | − | 1.42905i | −0.0768099 | − | 0.997046i | \(-0.524473\pi\) |
0.901872 | − | 0.432004i | \(-0.142193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.88914 | − | 2.24539i | −0.144839 | − | 0.0836228i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.4889 | 0.687608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.4877i | − | 1.16781i | −0.811821 | − | 0.583907i | \(-0.801523\pi\) | ||
0.811821 | − | 0.583907i | \(-0.198477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.1420 | 0.597853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.08112 | − | 3.60460i | −0.0769728 | − | 0.133321i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4714 | 1.56872 | 0.784359 | − | 0.620307i | \(-0.212992\pi\) | ||||
0.784359 | + | 0.620307i | \(0.212992\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.99201 | − | 1.15009i | −0.0733767 | − | 0.0423640i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.9368 | − | 6.89173i | 0.439103 | − | 0.253516i | −0.264114 | − | 0.964492i | \(-0.585079\pi\) |
0.703217 | + | 0.710975i | \(0.251746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.5000 | + | 7.76123i | 1.63475 | + | 0.285116i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.96961 | + | 13.8038i | 0.292377 | + | 0.506411i | 0.974371 | − | 0.224946i | \(-0.0722205\pi\) |
−0.681995 | + | 0.731357i | \(0.738887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.1721 | + | 29.7430i | −0.628296 | + | 1.08824i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.03787i | − | 0.257158i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.758540 | − | 1.31383i | −0.0276795 | − | 0.0479423i | 0.851854 | − | 0.523780i | \(-0.175478\pi\) |
−0.879533 | + | 0.475837i | \(0.842145\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 52.7610i | − | 1.92272i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.1214 | − | 23.7414i | 1.49458 | − | 0.862897i | 0.494601 | − | 0.869120i | \(-0.335314\pi\) |
0.999981 | + | 0.00622310i | \(0.00198089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.432748i | 0.0157078i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.3805 | − | 19.2722i | −1.21004 | − | 0.698618i | −0.247274 | − | 0.968946i | \(-0.579535\pi\) |
−0.962768 | + | 0.270327i | \(0.912868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.25697 | + | 3.03512i | 0.190315 | + | 0.109879i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.1258 | + | 16.8238i | 0.726700 | + | 0.607473i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5236 | + | 19.9322i | −1.24495 | + | 0.718775i | −0.970099 | − | 0.242711i | \(-0.921963\pi\) |
−0.274856 | + | 0.961486i | \(0.588630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.0817 | + | 52.1031i | −1.08337 | + | 1.87645i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.4774 | − | 28.5396i | 0.592650 | − | 1.02650i | −0.401224 | − | 0.915980i | \(-0.631415\pi\) |
0.993874 | − | 0.110519i | \(-0.0352514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.82878 | + | 1.05585i | −0.0656071 | + | 0.0378783i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.5352 | 1.48815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.71695 | −0.240351 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.55242 | − | 3.20569i | 0.198427 | − | 0.114562i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.539648 | − | 0.934698i | 0.0192364 | − | 0.0333184i | −0.856247 | − | 0.516567i | \(-0.827210\pi\) |
0.875483 | + | 0.483248i | \(0.160543\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.85480 | + | 3.21261i | −0.0660327 | + | 0.114372i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.08162 | + | 1.77917i | −0.109570 | + | 0.0632601i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0935 | + | 24.0372i | −0.713541 | + | 0.853584i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.5423 | − | 9.55071i | −0.585959 | − | 0.338304i | 0.177539 | − | 0.984114i | \(-0.443186\pi\) |
−0.763498 | + | 0.645810i | \(0.776520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.07744 | − | 1.19941i | −0.0734947 | − | 0.0424322i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.846678i | 0.0299159i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.3377 | + | 8.85521i | −0.541255 | + | 0.312494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 64.8896i | 2.28422i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.881702 | + | 1.52715i | 0.0309990 | + | 0.0536918i | 0.881109 | − | 0.472914i | \(-0.156798\pi\) |
−0.850110 | + | 0.526606i | \(0.823464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.3298i | 1.83755i | 0.394784 | + | 0.918774i | \(0.370819\pi\) | ||||
−0.394784 | + | 0.918774i | \(0.629181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.4044 | + | 47.4658i | −0.961113 | + | 1.66470i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1439 | − | 27.9621i | −0.564804 | − | 0.978270i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.20882 | + | 3.30209i | 0.0422397 | + | 0.115384i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3585 | + | 7.13517i | −0.431314 | + | 0.249019i | −0.699906 | − | 0.714235i | \(-0.746775\pi\) |
0.268592 | + | 0.963254i | \(0.413442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.8579 | − | 21.8573i | −1.31964 | − | 0.761896i | −0.335972 | − | 0.941872i | \(-0.609065\pi\) |
−0.983671 | + | 0.179976i | \(0.942398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.5962 | −0.785748 | −0.392874 | − | 0.919592i | \(-0.628519\pi\) | ||||
−0.392874 | + | 0.919592i | \(0.628519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.0473 | − | 46.8473i | −0.939392 | − | 1.62708i | −0.766608 | − | 0.642116i | \(-0.778057\pi\) |
−0.172784 | − | 0.984960i | \(-0.555276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.98914 | −0.242450 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.73668i | 0.164116i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.2835 | 0.355449 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2550 | − | 11.1169i | −0.664755 | − | 0.383796i | 0.129332 | − | 0.991601i | \(-0.458717\pi\) |
−0.794086 | + | 0.607805i | \(0.792050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.47796 | − | 4.29196i | 0.0854471 | − | 0.147999i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.6966 | − | 49.7039i | −0.988362 | − | 1.71189i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.59922 | − | 2.76993i | −0.0549498 | − | 0.0951758i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.52592 | − | 16.4994i | 0.326929 | − | 0.566257i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.210106 | − | 0.121305i | −0.00720235 | − | 0.00415828i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5312 | 0.566019 | 0.283009 | − | 0.959117i | \(-0.408667\pi\) | ||||
0.283009 | + | 0.959117i | \(0.408667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.5842i | 0.942259i | 0.882064 | + | 0.471129i | \(0.156154\pi\) | ||||
−0.882064 | + | 0.471129i | \(0.843846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.5016 | 1.10894 | 0.554469 | − | 0.832204i | \(-0.312921\pi\) | ||||
0.554469 | + | 0.832204i | \(0.312921\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.60485 | + | 6.24378i | 0.122853 | + | 0.212787i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.7986 | 1.01436 | 0.507178 | − | 0.861842i | \(-0.330689\pi\) | ||||
0.507178 | + | 0.861842i | \(0.330689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.3678 | − | 19.2649i | −1.13323 | − | 0.654270i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7300 | − | 11.3911i | 0.669294 | − | 0.386417i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.64603 | − | 4.49638i | −0.0557735 | − | 0.152354i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.7943 | − | 18.6962i | −0.365331 | − | 0.632772i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.20181 | − | 12.4739i | 0.243188 | − | 0.421214i | −0.718433 | − | 0.695597i | \(-0.755140\pi\) |
0.961621 | + | 0.274383i | \(0.0884735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.5004i | 0.590274i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.68457 | − | 6.38186i | −0.124136 | − | 0.215010i | 0.797259 | − | 0.603638i | \(-0.206283\pi\) |
−0.921395 | + | 0.388627i | \(0.872949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.3646i | − | 0.819933i | −0.912101 | − | 0.409967i | \(-0.865540\pi\) | ||
0.912101 | − | 0.409967i | \(-0.134460\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.8404 | + | 12.0322i | −0.699752 | + | 0.404002i | −0.807255 | − | 0.590203i | \(-0.799048\pi\) |
0.107503 | + | 0.994205i | \(0.465714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.86025i | − | 0.163008i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.5514 | + | 8.97859i | 0.520990 | + | 0.300794i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.1154 | − | 9.30426i | −0.539283 | − | 0.311355i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.577762 | + | 0.691157i | −0.0192909 | + | 0.0230771i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.3985 | + | 19.2826i | −1.11390 | + | 0.643112i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.05756 | − | 7.02790i | 0.135177 | − | 0.234133i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.80227 | − | 4.85367i | 0.0932537 | − | 0.161520i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4823 | + | 18.7536i | −1.07856 | + | 0.622705i | −0.930507 | − | 0.366275i | \(-0.880633\pi\) |
−0.148050 | + | 0.988980i | \(0.547300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0109 | 0.332039 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6000 | 0.417458 | 0.208729 | − | 0.977974i | \(-0.433067\pi\) | ||||
0.208729 | + | 0.977974i | \(0.433067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.1187 | + | 12.1929i | −0.698927 | + | 0.403526i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.423339 | − | 0.733244i | 0.0139799 | − | 0.0242139i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.8332 | + | 27.4239i | −0.522288 | + | 0.904630i | 0.477375 | + | 0.878699i | \(0.341588\pi\) |
−0.999664 | + | 0.0259305i | \(0.991745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0236 | − | 6.94185i | 0.396192 | − | 0.228742i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7279 | − | 8.96780i | −0.353112 | − | 0.295179i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.7292 | + | 13.7001i | 0.779371 | + | 0.449970i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.7537 | − | 14.8689i | −0.844952 | − | 0.487833i | 0.0139925 | − | 0.999902i | \(-0.495546\pi\) |
−0.858944 | + | 0.512069i | \(0.828879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.7441i | 1.20424i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.2040 | + | 20.9024i | −1.18527 | + | 0.684313i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 52.3124i | − | 1.70897i | −0.519474 | − | 0.854486i | \(-0.673872\pi\) | ||
0.519474 | − | 0.854486i | \(-0.326128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.8327 | + | 34.3512i | 0.647214 | + | 1.12101i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.5767i | 0.964174i | 0.876123 | + | 0.482087i | \(0.160121\pi\) | ||||
−0.876123 | + | 0.482087i | \(0.839879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.414157 | + | 0.717340i | −0.0134868 | + | 0.0233598i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.0165 | + | 41.5978i | 0.780432 | + | 1.35175i | 0.931690 | + | 0.363254i | \(0.118334\pi\) |
−0.151258 | + | 0.988494i | \(0.548332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.3189 | − | 6.33437i | −1.17896 | − | 0.205622i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.24720 | − | 3.60682i | 0.202579 | − | 0.116959i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.7923 | − | 14.8912i | −0.835494 | − | 0.482373i | 0.0202363 | − | 0.999795i | \(-0.493558\pi\) |
−0.855730 | + | 0.517423i | \(0.826891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.8079 | −0.640299 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.60485 | − | 6.24378i | −0.116407 | − | 0.201622i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8564 | −0.995368 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.9410i | 1.38376i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.6730 | −0.664798 | −0.332399 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332399 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.51336 | + | 4.33784i | 0.241364 | + | 0.139352i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.99307 | − | 17.3085i | 0.320693 | − | 0.555456i | −0.659938 | − | 0.751320i | \(-0.729418\pi\) |
0.980631 | + | 0.195863i | \(0.0627509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.96707 | − | 3.40706i | −0.0630613 | − | 0.109225i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.8138 | − | 39.5147i | −0.729878 | − | 1.26419i | −0.956934 | − | 0.290305i | \(-0.906243\pi\) |
0.227056 | − | 0.973882i | \(-0.427090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.300587 | + | 0.520632i | −0.00960680 | + | 0.0166395i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.0750 | − | 18.5185i | −1.02408 | − | 0.591251i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.1966 | −1.72860 | −0.864301 | − | 0.502975i | \(-0.832239\pi\) | ||||
−0.864301 | + | 0.502975i | \(0.832239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.23007i | − | 0.102814i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.643899 | 0.0204748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.2639 | − | 40.2943i | −0.739002 | − | 1.27999i | −0.952945 | − | 0.303143i | \(-0.901964\pi\) |
0.213943 | − | 0.976846i | \(-0.431369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.6440 | 1.67061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.8641 | + | 19.5514i | 1.07249 | + | 0.619200i | 0.928860 | − | 0.370432i | \(-0.120790\pi\) |
0.143626 | + | 0.989632i | \(0.454124\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.56441 | + | 1.48056i | −0.0811343 | + | 0.0468429i |
(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 | 1300.2.ba.c.49.3 | 8 | ||
5.2 | odd | 4 | 1300.2.y.b.101.1 | 8 | |||
5.3 | odd | 4 | 260.2.x.a.101.4 | ✓ | 8 | ||
5.4 | even | 2 | 1300.2.ba.b.49.2 | 8 | |||
13.4 | even | 6 | 1300.2.ba.b.849.2 | 8 | |||
15.8 | even | 4 | 2340.2.dj.d.361.1 | 8 | |||
20.3 | even | 4 | 1040.2.da.c.881.1 | 8 | |||
65.3 | odd | 12 | 3380.2.f.i.3041.2 | 8 | |||
65.4 | even | 6 | inner | 1300.2.ba.c.849.3 | 8 | ||
65.17 | odd | 12 | 1300.2.y.b.901.1 | 8 | |||
65.23 | odd | 12 | 3380.2.f.i.3041.1 | 8 | |||
65.28 | even | 12 | 3380.2.a.q.1.1 | 4 | |||
65.43 | odd | 12 | 260.2.x.a.121.4 | yes | 8 | ||
65.63 | even | 12 | 3380.2.a.p.1.1 | 4 | |||
195.173 | even | 12 | 2340.2.dj.d.901.3 | 8 | |||
260.43 | even | 12 | 1040.2.da.c.641.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.x.a.101.4 | ✓ | 8 | 5.3 | odd | 4 | ||
260.2.x.a.121.4 | yes | 8 | 65.43 | odd | 12 | ||
1040.2.da.c.641.1 | 8 | 260.43 | even | 12 | |||
1040.2.da.c.881.1 | 8 | 20.3 | even | 4 | |||
1300.2.y.b.101.1 | 8 | 5.2 | odd | 4 | |||
1300.2.y.b.901.1 | 8 | 65.17 | odd | 12 | |||
1300.2.ba.b.49.2 | 8 | 5.4 | even | 2 | |||
1300.2.ba.b.849.2 | 8 | 13.4 | even | 6 | |||
1300.2.ba.c.49.3 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.ba.c.849.3 | 8 | 65.4 | even | 6 | inner | ||
2340.2.dj.d.361.1 | 8 | 15.8 | even | 4 | |||
2340.2.dj.d.901.3 | 8 | 195.173 | even | 12 | |||
3380.2.a.p.1.1 | 4 | 65.63 | even | 12 | |||
3380.2.a.q.1.1 | 4 | 65.28 | even | 12 | |||
3380.2.f.i.3041.1 | 8 | 65.23 | odd | 12 | |||
3380.2.f.i.3041.2 | 8 | 65.3 | odd | 12 |