Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(505,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.1 | ||
Root | \(-0.766044 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.505 |
Dual form | 1368.2.s.j.577.1 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.87939 | + | 3.25519i | −0.840487 | + | 1.45577i | 0.0489972 | + | 0.998799i | \(0.484397\pi\) |
−0.889484 | + | 0.456967i | \(0.848936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.75877 | 1.79865 | 0.899323 | − | 0.437285i | \(-0.144060\pi\) | ||||
0.899323 | + | 0.437285i | \(0.144060\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.36959 | 1.31748 | 0.658740 | − | 0.752371i | \(-0.271090\pi\) | ||||
0.658740 | + | 0.752371i | \(0.271090\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.06418 | − | 5.30731i | 0.743172 | − | 1.28721i | −0.207872 | − | 0.978156i | \(-0.566654\pi\) |
0.951044 | − | 0.309056i | \(-0.100013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.694593 | + | 4.30320i | 0.159350 | + | 0.987222i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.87939 | − | 3.25519i | −0.391879 | − | 0.678754i | 0.600818 | − | 0.799385i | \(-0.294841\pi\) |
−0.992697 | + | 0.120631i | \(0.961508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.56418 | − | 7.90539i | −0.912836 | − | 1.58108i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.69459 | + | 4.66717i | 0.500373 | + | 0.866672i | 1.00000 | 0.000431109i | \(0.000137226\pi\) | |
−0.499627 | + | 0.866241i | \(0.666529\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.36959 | 1.32362 | 0.661808 | − | 0.749673i | \(-0.269789\pi\) | ||||
0.661808 | + | 0.749673i | \(0.269789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.94356 | + | 15.4907i | −1.51174 | + | 2.61841i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.12836 | −1.17189 | −0.585947 | − | 0.810349i | \(-0.699277\pi\) | ||||
−0.585947 | + | 0.810349i | \(0.699277\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.75877 | + | 3.04628i | −0.274674 | + | 0.475749i | −0.970053 | − | 0.242894i | \(-0.921903\pi\) |
0.695379 | + | 0.718643i | \(0.255237\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.379385 | − | 0.657115i | 0.0578557 | − | 0.100209i | −0.835647 | − | 0.549267i | \(-0.814907\pi\) |
0.893503 | + | 0.449058i | \(0.148240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.6459 | 2.23513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.57398 | + | 4.45826i | 0.353563 | + | 0.612389i | 0.986871 | − | 0.161511i | \(-0.0516366\pi\) |
−0.633308 | + | 0.773900i | \(0.718303\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.21213 | + | 14.2238i | −1.10732 | + | 1.91794i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.63816 | − | 8.03352i | 0.603836 | − | 1.04588i | −0.388398 | − | 0.921492i | \(-0.626971\pi\) |
0.992234 | − | 0.124384i | \(-0.0396953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.25877 | + | 7.37641i | 0.545280 | + | 0.944452i | 0.998589 | + | 0.0530990i | \(0.0169099\pi\) |
−0.453310 | + | 0.891353i | \(0.649757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.75877 | 0.466218 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.684793 | − | 1.18610i | −0.0836607 | − | 0.144905i | 0.821159 | − | 0.570699i | \(-0.193328\pi\) |
−0.904820 | + | 0.425795i | \(0.859995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.82295 | + | 10.0856i | −0.691057 | + | 1.19695i | 0.280435 | + | 0.959873i | \(0.409521\pi\) |
−0.971492 | + | 0.237073i | \(0.923812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.25877 | + | 3.91231i | −0.264369 | + | 0.457901i | −0.967398 | − | 0.253260i | \(-0.918497\pi\) |
0.703029 | + | 0.711161i | \(0.251830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.7939 | 2.36968 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.07398 | + | 12.2525i | −0.795885 | + | 1.37851i | 0.126391 | + | 0.991980i | \(0.459661\pi\) |
−0.922276 | + | 0.386532i | \(0.873673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.90673 | −0.538583 | −0.269292 | − | 0.963059i | \(-0.586790\pi\) | ||||
−0.269292 | + | 0.963059i | \(0.586790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5175 | + | 19.9490i | 1.24925 | + | 2.16377i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.18479 | + | 7.24827i | 0.443587 | + | 0.768315i | 0.997953 | − | 0.0639579i | \(-0.0203723\pi\) |
−0.554365 | + | 0.832273i | \(0.687039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.37939 | − | 4.12122i | −0.249427 | − | 0.432021i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.3131 | − | 5.82634i | −1.57110 | − | 0.597770i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.82295 | − | 10.0856i | 0.591231 | − | 1.02404i | −0.402836 | − | 0.915272i | \(-0.631976\pi\) |
0.994067 | − | 0.108770i | \(-0.0346911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.06418 | − | 3.57526i | −0.205393 | − | 0.355752i | 0.744865 | − | 0.667216i | \(-0.232514\pi\) |
−0.950258 | + | 0.311464i | \(0.899181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.75877 | −0.665961 | −0.332981 | − | 0.942934i | \(-0.608054\pi\) | ||||
−0.332981 | + | 0.942934i | \(0.608054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.12836 | 0.399103 | 0.199552 | − | 0.979887i | \(-0.436051\pi\) | ||||
0.199552 | + | 0.979887i | \(0.436051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0641778 | − | 0.111159i | 0.00614712 | − | 0.0106471i | −0.862935 | − | 0.505314i | \(-0.831377\pi\) |
0.869083 | + | 0.494667i | \(0.164710\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.40879 | 0.226600 | 0.113300 | − | 0.993561i | \(-0.463858\pi\) | ||||
0.113300 | + | 0.993561i | \(0.463858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1284 | 1.31748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.5817 | − | 25.2563i | 1.33670 | − | 2.31524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.09327 | 0.735752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15.5175 | 1.38793 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.241230 | − | 0.417822i | −0.0214057 | − | 0.0370757i | 0.855124 | − | 0.518423i | \(-0.173481\pi\) |
−0.876530 | + | 0.481348i | \(0.840147\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.69459 | + | 2.93512i | −0.148057 | + | 0.256443i | −0.930509 | − | 0.366268i | \(-0.880635\pi\) |
0.782452 | + | 0.622711i | \(0.213969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.30541 | + | 20.4779i | 0.286615 | + | 1.77566i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.21213 | − | 15.9559i | −0.787046 | − | 1.36320i | −0.927769 | − | 0.373154i | \(-0.878276\pi\) |
0.140724 | − | 0.990049i | \(-0.455057\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.00980018 | − | 0.0169744i | −0.000831240 | − | 0.00143975i | 0.865609 | − | 0.500720i | \(-0.166931\pi\) |
−0.866441 | + | 0.499280i | \(0.833598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.18479 | − | 3.78417i | −0.182702 | − | 0.316448i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.2567 | −1.68223 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.12061 | − | 5.40506i | 0.255651 | − | 0.442800i | −0.709421 | − | 0.704785i | \(-0.751044\pi\) |
0.965072 | + | 0.261985i | \(0.0843770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.739170 | 0.0601528 | 0.0300764 | − | 0.999548i | \(-0.490425\pi\) | ||||
0.0300764 | + | 0.999548i | \(0.490425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.8503 | + | 23.9894i | −1.11248 | + | 1.92688i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.32295 | − | 5.75552i | 0.265200 | − | 0.459340i | −0.702416 | − | 0.711767i | \(-0.747895\pi\) |
0.967616 | + | 0.252427i | \(0.0812286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.94356 | − | 15.4907i | −0.704852 | − | 1.22084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3696 | −0.890535 | −0.445267 | − | 0.895398i | \(-0.646891\pi\) | ||||
−0.445267 | + | 0.895398i | \(0.646891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.49020 | + | 2.58110i | 0.115315 | + | 0.199732i | 0.917906 | − | 0.396799i | \(-0.129879\pi\) |
−0.802591 | + | 0.596530i | \(0.796546\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.69459 | + | 4.66717i | −0.204866 | + | 0.354838i | −0.950090 | − | 0.311976i | \(-0.899009\pi\) |
0.745224 | + | 0.666814i | \(0.232343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7199 | − | 37.6199i | −1.64187 | − | 2.84380i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.24123 | −0.317004 | −0.158502 | − | 0.987359i | \(-0.550666\pi\) | ||||
−0.158502 | + | 0.987359i | \(0.550666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.30541 | − | 10.9213i | −0.468677 | − | 0.811773i | 0.530682 | − | 0.847571i | \(-0.321936\pi\) |
−0.999359 | + | 0.0357984i | \(0.988603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.3969 | − | 23.2042i | 0.984962 | − | 1.70600i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3892 | − | 23.1907i | 0.979114 | − | 1.69588i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6263 | 1.63718 | 0.818591 | − | 0.574377i | \(-0.194756\pi\) | ||||
0.818591 | + | 0.574377i | \(0.194756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3229 | + | 21.3440i | −0.887025 | + | 1.53637i | −0.0436505 | + | 0.999047i | \(0.513899\pi\) |
−0.843375 | + | 0.537326i | \(0.819435\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.6655 | −1.61485 | −0.807425 | − | 0.589970i | \(-0.799139\pi\) | ||||
−0.807425 | + | 0.589970i | \(0.799139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.96110 | − | 12.0570i | −0.493460 | − | 0.854697i | 0.506512 | − | 0.862233i | \(-0.330935\pi\) |
−0.999972 | + | 0.00753584i | \(0.997601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8229 | + | 22.2100i | 0.899995 | + | 1.55884i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.61081 | − | 11.4503i | −0.461719 | − | 0.799721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.03508 | + | 18.8032i | 0.209941 | + | 1.30064i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00980 | − | 1.74903i | 0.0695175 | − | 0.120408i | −0.829172 | − | 0.558994i | \(-0.811187\pi\) |
0.898689 | + | 0.438586i | \(0.144521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.42602 | + | 2.46994i | 0.0972539 | + | 0.168449i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.0702 | 2.38072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.12836 | −0.412238 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1827 | + | 24.5652i | −0.949746 | + | 1.64501i | −0.203789 | + | 0.979015i | \(0.565325\pi\) |
−0.745958 | + | 0.665993i | \(0.768008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.1830 | −1.33960 | −0.669798 | − | 0.742544i | \(-0.733619\pi\) | ||||
−0.669798 | + | 0.742544i | \(0.733619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7784 | 0.778337 | 0.389168 | − | 0.921167i | \(-0.372762\pi\) | ||||
0.389168 | + | 0.921167i | \(0.372762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0641778 | + | 0.111159i | −0.00420443 | + | 0.00728228i | −0.868120 | − | 0.496354i | \(-0.834672\pi\) |
0.863916 | + | 0.503637i | \(0.168005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.5526 | 1.47117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.10876 | −0.201089 | −0.100544 | − | 0.994933i | \(-0.532058\pi\) | ||||
−0.100544 | + | 0.994933i | \(0.532058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.64796 | − | 9.78255i | −0.363817 | − | 0.630149i | 0.624769 | − | 0.780810i | \(-0.285193\pi\) |
−0.988586 | + | 0.150661i | \(0.951860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.4047 | + | 50.9304i | −1.87860 | + | 3.25382i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.37939 | − | 2.75314i | 0.215025 | − | 0.175178i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.758770 | − | 1.31423i | −0.0478932 | − | 0.0829534i | 0.841085 | − | 0.540903i | \(-0.181917\pi\) |
−0.888978 | + | 0.457950i | \(0.848584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.21213 | − | 14.2238i | −0.516292 | − | 0.894245i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.09152 | − | 10.5508i | −0.379979 | − | 0.658142i | 0.611080 | − | 0.791569i | \(-0.290735\pi\) |
−0.991059 | + | 0.133427i | \(0.957402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.9222 | −2.10782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.69459 | + | 16.7915i | −0.597794 | + | 1.03541i | 0.395352 | + | 0.918530i | \(0.370623\pi\) |
−0.993146 | + | 0.116880i | \(0.962711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.3500 | −1.18866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7023 | − | 20.2690i | 0.713504 | − | 1.23582i | −0.250030 | − | 0.968238i | \(-0.580440\pi\) |
0.963534 | − | 0.267587i | \(-0.0862262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.482459 | + | 0.835644i | −0.0293073 | + | 0.0507617i | −0.880307 | − | 0.474404i | \(-0.842663\pi\) |
0.851000 | + | 0.525166i | \(0.175997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.9436 | − | 34.5433i | −1.20264 | − | 2.08304i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3892 | 0.924647 | 0.462323 | − | 0.886711i | \(-0.347016\pi\) | ||||
0.462323 | + | 0.886711i | \(0.347016\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.24897 | + | 7.35943i | 0.253472 | + | 0.439027i | 0.964479 | − | 0.264158i | \(-0.0850940\pi\) |
−0.711007 | + | 0.703185i | \(0.751761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.51754 | − | 9.55666i | 0.327984 | − | 0.568085i | −0.654128 | − | 0.756384i | \(-0.726964\pi\) |
0.982112 | + | 0.188299i | \(0.0602975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.36959 | + | 14.4965i | −0.494041 | + | 0.855704i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2784 | − | 17.8027i | −0.604610 | − | 1.04722i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.03508 | 0.0604701 | 0.0302351 | − | 0.999543i | \(-0.490374\pi\) | ||||
0.0302351 | + | 0.999543i | \(0.490374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4338 | + | 30.1962i | 1.01503 | + | 1.75809i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.87939 | + | 3.25519i | −0.108688 | + | 0.188253i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.80541 | − | 3.12706i | 0.104062 | − | 0.180241i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.0155 | −1.83320 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.43376 | + | 12.8757i | −0.424267 | + | 0.734852i | −0.996352 | − | 0.0853423i | \(-0.972802\pi\) |
0.572084 | + | 0.820195i | \(0.306135\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0547 | 0.910378 | 0.455189 | − | 0.890395i | \(-0.349572\pi\) | ||||
0.455189 | + | 0.890395i | \(0.349572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5817 | − | 30.4524i | −0.993777 | − | 1.72127i | −0.593350 | − | 0.804945i | \(-0.702195\pi\) |
−0.400428 | − | 0.916328i | \(-0.631138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.26857 | + | 16.0536i | 0.520575 | + | 0.901662i | 0.999714 | + | 0.0239230i | \(0.00761564\pi\) |
−0.479139 | + | 0.877739i | \(0.659051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7743 | + | 20.3936i | 0.659232 | + | 1.14182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.9668 | + | 9.49935i | 1.38919 | + | 0.528558i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56418 | + | 7.90539i | −0.253175 | + | 0.438512i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.2763 | − | 24.7273i | −0.787079 | − | 1.36326i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.75877 | −0.481426 | −0.240713 | − | 0.970596i | \(-0.577381\pi\) | ||||
−0.240713 | + | 0.970596i | \(0.577381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.14796 | 0.281263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6925 | − | 18.5200i | 0.582459 | − | 1.00885i | −0.412728 | − | 0.910855i | \(-0.635424\pi\) |
0.995187 | − | 0.0979947i | \(-0.0312428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.2020 | 1.74384 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 41.1438 | 2.22156 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.9632 | − | 20.7208i | 0.642216 | − | 1.11235i | −0.342721 | − | 0.939437i | \(-0.611348\pi\) |
0.984937 | − | 0.172914i | \(-0.0553182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.0702 | −1.23492 | −0.617459 | − | 0.786603i | \(-0.711838\pi\) | ||||
−0.617459 | + | 0.786603i | \(0.711838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4979 | 1.51679 | 0.758396 | − | 0.651794i | \(-0.225983\pi\) | ||||
0.758396 | + | 0.651794i | \(0.225983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8871 | − | 37.9096i | −1.16165 | − | 2.01203i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.48246 | − | 4.29975i | 0.131019 | − | 0.226932i | −0.793051 | − | 0.609156i | \(-0.791508\pi\) |
0.924070 | + | 0.382224i | \(0.124842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0351 | + | 5.97794i | −0.949215 | + | 0.314629i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.49020 | − | 14.7055i | −0.444397 | − | 0.769719i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.42396 | − | 16.3228i | −0.491927 | − | 0.852042i | 0.508030 | − | 0.861339i | \(-0.330374\pi\) |
−0.999957 | + | 0.00929712i | \(0.997041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2490 | + | 21.2158i | 0.635935 | + | 1.10147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9026 | 1.85897 | 0.929483 | − | 0.368864i | \(-0.120253\pi\) | ||||
0.929483 | + | 0.368864i | \(0.120253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.69459 | − | 4.66717i | 0.138779 | − | 0.240372i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2763 | −0.630592 | −0.315296 | − | 0.948993i | \(-0.602104\pi\) | ||||
−0.315296 | + | 0.948993i | \(0.602104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.20439 | − | 12.4784i | 0.368127 | − | 0.637615i | −0.621145 | − | 0.783695i | \(-0.713332\pi\) |
0.989273 | + | 0.146080i | \(0.0466657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −39.0797 | + | 67.6880i | −1.99168 | + | 3.44970i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.18479 | + | 5.51622i | 0.161475 | + | 0.279684i | 0.935398 | − | 0.353597i | \(-0.115041\pi\) |
−0.773923 | + | 0.633280i | \(0.781708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.0351 | −1.16493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.5895 | − | 46.0543i | −1.33786 | − | 2.31724i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.27837 | − | 9.14241i | 0.264914 | − | 0.458844i | −0.702627 | − | 0.711558i | \(-0.747990\pi\) |
0.967541 | + | 0.252714i | \(0.0813231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.7219 | − | 18.5709i | 0.535428 | − | 0.927388i | −0.463715 | − | 0.885985i | \(-0.653484\pi\) |
0.999143 | − | 0.0414036i | \(-0.0131829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68479 | − | 6.38225i | −0.183553 | − | 0.317922i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.1480 | −1.54395 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.32501 | − | 5.75908i | −0.164411 | − | 0.284768i | 0.772035 | − | 0.635580i | \(-0.219239\pi\) |
−0.936446 | + | 0.350812i | \(0.885906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.0719 | − | 38.2297i | 1.08609 | − | 1.88116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.22163 | − | 15.9723i | 0.452672 | − | 0.784051i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.84793 | −0.285690 | −0.142845 | − | 0.989745i | \(-0.545625\pi\) | ||||
−0.142845 | + | 0.989745i | \(0.545625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.714193 | + | 1.23702i | −0.0348076 | + | 0.0602886i | −0.882904 | − | 0.469553i | \(-0.844415\pi\) |
0.848097 | + | 0.529841i | \(0.177749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −55.9418 | −2.71358 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.2665 | + | 35.1026i | 0.980765 | + | 1.69874i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.389185 | + | 0.674089i | 0.0187464 | + | 0.0324697i | 0.875246 | − | 0.483677i | \(-0.160699\pi\) |
−0.856500 | + | 0.516147i | \(0.827366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.3425 | − | 23.1100i | −0.641202 | − | 1.11059i | −0.985165 | − | 0.171611i | \(-0.945103\pi\) |
0.343963 | − | 0.938983i | \(-0.388231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.7023 | − | 10.3484i | 0.607635 | − | 0.495031i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2665 | − | 24.7103i | 0.680903 | − | 1.17936i | −0.293802 | − | 0.955866i | \(-0.594921\pi\) |
0.974706 | − | 0.223493i | \(-0.0717460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.82295 | − | 15.2818i | −0.419191 | − | 0.726060i | 0.576667 | − | 0.816979i | \(-0.304353\pi\) |
−0.995858 | + | 0.0909191i | \(0.971020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.4593 | −1.49132 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.38919 | 0.0655597 | 0.0327799 | − | 0.999463i | \(-0.489564\pi\) | ||||
0.0327799 | + | 0.999463i | \(0.489564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.68510 | + | 13.3110i | −0.361877 | + | 0.626790i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8871 | 0.838561 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6851 | 1.15472 | 0.577360 | − | 0.816490i | \(-0.304083\pi\) | ||||
0.577360 | + | 0.816490i | \(0.304083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.795607 | − | 1.37803i | 0.0370551 | − | 0.0641813i | −0.846903 | − | 0.531747i | \(-0.821536\pi\) |
0.883958 | + | 0.467566i | \(0.154869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.7547 | −1.01102 | −0.505512 | − | 0.862819i | \(-0.668696\pi\) | ||||
−0.505512 | + | 0.862819i | \(0.668696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.5175 | −0.718066 | −0.359033 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359033 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25877 | − | 5.64436i | −0.150476 | − | 0.260632i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.65776 | − | 2.87132i | 0.0762237 | − | 0.132023i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.8482 | − | 25.1316i | 1.41541 | − | 1.15312i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.82295 | − | 10.0856i | −0.266057 | − | 0.460825i | 0.701783 | − | 0.712391i | \(-0.252388\pi\) |
−0.967840 | + | 0.251566i | \(0.919054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.56418 | + | 6.17334i | 0.162513 | + | 0.281480i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.8871 | + | 37.9096i | 0.993843 | + | 1.72139i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.5526 | 1.74699 | 0.873493 | − | 0.486837i | \(-0.161849\pi\) | ||||
0.873493 | + | 0.486837i | \(0.161849\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.82295 | − | 6.62154i | 0.172527 | − | 0.298826i | −0.766776 | − | 0.641915i | \(-0.778140\pi\) |
0.939303 | + | 0.343089i | \(0.111473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.0268 | 1.48745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.7101 | + | 47.9953i | −1.24297 | + | 2.15288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3152 | + | 26.5267i | −0.685603 | + | 1.18750i | 0.287644 | + | 0.957737i | \(0.407128\pi\) |
−0.973247 | + | 0.229762i | \(0.926205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.69459 | − | 4.66717i | −0.120146 | − | 0.208099i | 0.799679 | − | 0.600428i | \(-0.205003\pi\) |
−0.919825 | + | 0.392329i | \(0.871670\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5175 | 0.690522 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.12836 | − | 1.95437i | −0.0500135 | − | 0.0866259i | 0.839935 | − | 0.542687i | \(-0.182593\pi\) |
−0.889948 | + | 0.456061i | \(0.849260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7490 | + | 18.6178i | −0.475506 | + | 0.823601i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7023 | − | 22.0011i | 0.559732 | − | 0.969484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1088 | − | 22.7050i | −0.576522 | − | 0.998566i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.2763 | −1.63310 | −0.816552 | − | 0.577271i | \(-0.804118\pi\) | ||||
−0.816552 | + | 0.577271i | \(0.804118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.186852 | + | 0.323637i | 0.00817046 | + | 0.0141517i | 0.870082 | − | 0.492907i | \(-0.164066\pi\) |
−0.861911 | + | 0.507059i | \(0.830733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.5817 | − | 39.1127i | 0.983675 | − | 1.70378i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.43582 | − | 7.68307i | 0.192862 | − | 0.334046i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.51754 | 0.152362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.75877 | + | 13.4386i | −0.335441 | + | 0.581001i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 68.3661 | 2.94474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.54458 | + | 16.5317i | 0.410353 | + | 0.710753i | 0.994928 | − | 0.100587i | \(-0.0320720\pi\) |
−0.584575 | + | 0.811340i | \(0.698739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.241230 | + | 0.417822i | 0.0103331 | + | 0.0178975i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.8773 | − | 37.8926i | −0.935407 | − | 1.62017i | −0.773907 | − | 0.633300i | \(-0.781700\pi\) |
−0.161500 | − | 0.986873i | \(-0.551633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.2121 | + | 14.8372i | −0.775863 | + | 0.632084i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.6634 | + | 58.3068i | −1.43151 | + | 2.47946i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9513 | + | 27.6285i | 0.675878 | + | 1.17066i | 0.976211 | + | 0.216821i | \(0.0695689\pi\) |
−0.300333 | + | 0.953834i | \(0.597098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.758770 | −0.0320926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.87164 | 0.163170 | 0.0815852 | − | 0.996666i | \(-0.474002\pi\) | ||||
0.0815852 | + | 0.996666i | \(0.474002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.52704 | + | 7.84106i | −0.190454 | + | 0.329876i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.9959 | 1.38326 | 0.691630 | − | 0.722252i | \(-0.256893\pi\) | ||||
0.691630 | + | 0.722252i | \(0.256893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.1789 | −1.01186 | −0.505928 | − | 0.862576i | \(-0.668850\pi\) | ||||
−0.505928 | + | 0.862576i | \(0.668850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.1557 | + | 29.7145i | −0.715442 | + | 1.23918i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.16344 | −0.131696 | −0.0658478 | − | 0.997830i | \(-0.520975\pi\) | ||||
−0.0658478 | + | 0.997830i | \(0.520975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.3500 | −0.968721 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2472 | + | 19.4807i | 0.465812 | + | 0.806810i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.00774 | + | 5.20956i | −0.124143 | + | 0.215022i | −0.921398 | − | 0.388621i | \(-0.872951\pi\) |
0.797255 | + | 0.603643i | \(0.206285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.11886 | + | 31.7128i | 0.210919 | + | 1.30670i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4611 | + | 19.8512i | 0.470651 | + | 0.815192i | 0.999437 | − | 0.0335639i | \(-0.0106857\pi\) |
−0.528785 | + | 0.848756i | \(0.677352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 54.8093 | + | 94.9326i | 2.24696 | + | 3.89186i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.2199 | + | 29.8257i | 0.703585 | + | 1.21864i | 0.967200 | + | 0.254017i | \(0.0817519\pi\) |
−0.263615 | + | 0.964628i | \(0.584915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1634 | 0.985647 | 0.492824 | − | 0.870129i | \(-0.335965\pi\) | ||||
0.492824 | + | 0.870129i | \(0.335965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.2104 | + | 26.3451i | −0.618390 | + | 1.07108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.84793 | −0.277949 | −0.138974 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138974 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | + | 5.19615i | −0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.47296 | + | 14.6756i | −0.342220 | + | 0.592742i | −0.984845 | − | 0.173439i | \(-0.944512\pi\) |
0.642625 | + | 0.766181i | \(0.277845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1361 | + | 36.6088i | 0.850907 | + | 1.47381i | 0.880391 | + | 0.474249i | \(0.157280\pi\) |
−0.0294834 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.59121 | 0.184536 | 0.0922682 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922682 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.9145 | + | 34.4929i | 0.797856 | + | 1.38193i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.34255 | + | 10.9856i | −0.253702 | + | 0.439425i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.8425 | + | 37.8324i | −0.870919 | + | 1.50848i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.7841 | + | 32.5349i | 0.747781 | + | 1.29520i | 0.948884 | + | 0.315625i | \(0.102214\pi\) |
−0.201103 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.81345 | 0.0719647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.82295 | − | 13.5497i | −0.309956 | − | 0.536860i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.75877 | + | 4.77833i | −0.108965 | + | 0.188733i | −0.915351 | − | 0.402656i | \(-0.868087\pi\) |
0.806386 | + | 0.591389i | \(0.201420\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.5915 | − | 30.4694i | 0.693742 | − | 1.20160i | −0.276861 | − | 0.960910i | \(-0.589294\pi\) |
0.970603 | − | 0.240686i | \(-0.0773724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.57573 | 0.140577 | 0.0702883 | − | 0.997527i | \(-0.477608\pi\) | ||||
0.0702883 | + | 0.997527i | \(0.477608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2668 | − | 35.1032i | 0.795542 | − | 1.37792i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.6418 | −1.27737 | −0.638686 | − | 0.769468i | \(-0.720522\pi\) | ||||
−0.638686 | + | 0.769468i | \(0.720522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.36959 | − | 11.0324i | −0.248880 | − | 0.431073i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4807 | + | 42.4018i | 0.953633 | + | 1.65174i | 0.737466 | + | 0.675384i | \(0.236022\pi\) |
0.216167 | + | 0.976356i | \(0.430645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7392 | − | 30.7251i | −0.689974 | − | 1.19507i | −0.971846 | − | 0.235618i | \(-0.924289\pi\) |
0.281872 | − | 0.959452i | \(-0.409045\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −72.8718 | − | 27.7262i | −2.82585 | − | 1.07518i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1284 | − | 17.5428i | 0.392171 | − | 0.679261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.6091 | + | 32.2318i | 0.718395 | + | 1.24430i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.68510 | 0.103503 | 0.0517514 | − | 0.998660i | \(-0.483520\pi\) | ||||
0.0517514 | + | 0.998660i | \(0.483520\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3351 | −0.704676 | −0.352338 | − | 0.935873i | \(-0.614613\pi\) | ||||
−0.352338 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7101 | − | 47.9953i | 1.06342 | − | 1.84189i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.07367 | −0.155875 | −0.0779374 | − | 0.996958i | \(-0.524833\pi\) | ||||
−0.0779374 | + | 0.996958i | \(0.524833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 69.2526 | 2.64601 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.57398 | − | 4.45826i | 0.0980608 | − | 0.169846i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.5485 | 1.65666 | 0.828332 | − | 0.560238i | \(-0.189290\pi\) | ||||
0.828332 | + | 0.560238i | \(0.189290\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0736733 | 0.00279459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7784 | + | 18.6687i | 0.408260 | + | 0.707127i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6536 | − | 27.1129i | 0.591230 | − | 1.02404i | −0.402837 | − | 0.915272i | \(-0.631976\pi\) |
0.994067 | − | 0.108768i | \(-0.0346907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.95130 | − | 30.6747i | −0.186742 | − | 1.15692i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.82295 | − | 17.0138i | −0.369430 | − | 0.639872i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9047 | − | 20.6195i | −0.447089 | − | 0.774381i | 0.551106 | − | 0.834435i | \(-0.314206\pi\) |
−0.998195 | + | 0.0600541i | \(0.980873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8503 | − | 23.9894i | −0.518697 | − | 0.898410i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.4243 | 0.614233 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.8949 | − | 27.5307i | 0.592779 | − | 1.02672i | −0.401078 | − | 0.916044i | \(-0.631364\pi\) |
0.993856 | − | 0.110678i | \(-0.0353024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.1634 | −1.19783 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.5972 | − | 42.6036i | 0.913517 | − | 1.58226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.22193 | − | 5.58055i | 0.119495 | − | 0.206971i | −0.800073 | − | 0.599903i | \(-0.795206\pi\) |
0.919568 | + | 0.392932i | \(0.128539\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.32501 | − | 4.02703i | −0.0859935 | − | 0.148945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.9728 | −1.25481 | −0.627406 | − | 0.778692i | \(-0.715884\pi\) | ||||
−0.627406 | + | 0.778692i | \(0.715884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.99226 | − | 5.18274i | −0.110221 | − | 0.190909i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.4632 | + | 19.8548i | −0.421679 | + | 0.730370i | −0.996104 | − | 0.0881876i | \(-0.971893\pi\) |
0.574425 | + | 0.818557i | \(0.305226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.98276 | + | 6.89835i | −0.146113 | + | 0.253076i | −0.929788 | − | 0.368096i | \(-0.880010\pi\) |
0.783674 | + | 0.621172i | \(0.213343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7297 | + | 20.3164i | 0.429742 | + | 0.744335i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.6459 | 0.717845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.3794 | + | 19.7097i | 0.415240 | + | 0.719216i | 0.995454 | − | 0.0952479i | \(-0.0303644\pi\) |
−0.580214 | + | 0.814464i | \(0.697031\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.38919 | + | 2.40614i | −0.0505576 | + | 0.0875684i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.38713 | + | 4.13462i | −0.0867616 | + | 0.150275i | −0.906140 | − | 0.422977i | \(-0.860985\pi\) |
0.819379 | + | 0.573252i | \(0.194318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.2222 | −1.02306 | −0.511528 | − | 0.859267i | \(-0.670920\pi\) | ||||
−0.511528 | + | 0.859267i | \(0.670920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.305407 | − | 0.528981i | 0.0110565 | − | 0.0191504i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.27631 | −0.334948 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1108 | − | 20.9765i | −0.436727 | − | 0.756434i | 0.560708 | − | 0.828014i | \(-0.310529\pi\) |
−0.997435 | + | 0.0715802i | \(0.977196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9804 | + | 20.7507i | 0.430905 | + | 0.746349i | 0.996951 | − | 0.0780239i | \(-0.0248611\pi\) |
−0.566046 | + | 0.824373i | \(0.691528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.6361 | − | 58.2594i | −1.20824 | − | 2.09274i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.3304 | − | 5.45242i | −0.513439 | − | 0.195353i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.4439 | + | 44.0701i | −0.910453 | + | 1.57695i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4902 | + | 21.6337i | 0.445794 | + | 0.772138i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.8871 | −1.02971 | −0.514857 | − | 0.857276i | \(-0.672155\pi\) | ||||
−0.514857 | + | 0.857276i | \(0.672155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4629 | 0.407572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.25877 | − | 7.37641i | 0.151233 | − | 0.261944i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.61493 | 0.269735 | 0.134867 | − | 0.990864i | \(-0.456939\pi\) | ||||
0.134867 | + | 0.990864i | \(0.456939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.7701 | −1.30083 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.86989 | + | 17.0952i | −0.348301 | + | 0.603275i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.2336 | 2.36967 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5681 | −0.793452 | −0.396726 | − | 0.917937i | \(-0.629854\pi\) | ||||
−0.396726 | + | 0.917937i | \(0.629854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.3696 | + | 21.4247i | 0.434355 | + | 0.752325i | 0.997243 | − | 0.0742086i | \(-0.0236431\pi\) |
−0.562888 | + | 0.826533i | \(0.690310\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.3678 | − | 37.0102i | 0.748482 | − | 1.29641i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.09121 | + | 1.17614i | 0.108148 | + | 0.0411481i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.30541 | − | 16.1174i | −0.324761 | − | 0.562502i | 0.656703 | − | 0.754149i | \(-0.271951\pi\) |
−0.981464 | + | 0.191647i | \(0.938617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.9804 | + | 19.0186i | 0.382753 | + | 0.662947i | 0.991455 | − | 0.130452i | \(-0.0416428\pi\) |
−0.608702 | + | 0.793399i | \(0.708309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9513 | − | 22.4323i | −0.450361 | − | 0.780048i | 0.548047 | − | 0.836447i | \(-0.315371\pi\) |
−0.998408 | + | 0.0563993i | \(0.982038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.0310 | −1.49453 | −0.747264 | − | 0.664528i | \(-0.768633\pi\) | ||||
−0.747264 | + | 0.664528i | \(0.768633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.9418 | − | 83.0376i | 1.66109 | − | 2.87708i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2026 | −0.387683 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.16519 | − | 7.21432i | 0.143798 | − | 0.249066i | −0.785126 | − | 0.619337i | \(-0.787402\pi\) |
0.928924 | + | 0.370270i | \(0.120735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0216598 | + | 0.0375158i | −0.000746888 | + | 0.00129365i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.5526 | + | 39.0623i | 0.775834 | + | 1.34378i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.5140 | 1.32336 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.3969 | + | 23.2042i | 0.459241 | + | 0.795428i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6925 | − | 37.5726i | 0.742738 | − | 1.28646i | −0.208506 | − | 0.978021i | \(-0.566860\pi\) |
0.951244 | − | 0.308439i | \(-0.0998066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.2567 | − | 29.8895i | 0.589478 | − | 1.02101i | −0.404823 | − | 0.914395i | \(-0.632667\pi\) |
0.994301 | − | 0.106611i | \(-0.0339999\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.08946 | + | 15.7434i | 0.310128 | + | 0.537158i | 0.978390 | − | 0.206768i | \(-0.0662946\pi\) |
−0.668262 | + | 0.743926i | \(0.732961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.3269 | −1.50890 | −0.754452 | − | 0.656355i | \(-0.772097\pi\) | ||||
−0.754452 | + | 0.656355i | \(0.772097\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1284 | − | 17.5428i | −0.344374 | − | 0.596474i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.9103 | + | 53.5383i | −1.04856 | + | 1.81616i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.684793 | + | 1.18610i | −0.0232033 | + | 0.0401893i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 73.8444 | 2.49640 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.95336 | + | 10.3115i | −0.201031 | + | 0.348196i | −0.948861 | − | 0.315695i | \(-0.897762\pi\) |
0.747830 | + | 0.663890i | \(0.231096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.9804 | −0.976374 | −0.488187 | − | 0.872739i | \(-0.662342\pi\) | ||||
−0.488187 | + | 0.872739i | \(0.662342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.23143 | − | 3.86495i | −0.0750936 | − | 0.130066i | 0.826033 | − | 0.563621i | \(-0.190592\pi\) |
−0.901127 | + | 0.433555i | \(0.857259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.1557 | − | 24.5184i | −0.475302 | − | 0.823247i | 0.524298 | − | 0.851535i | \(-0.324328\pi\) |
−0.999600 | + | 0.0282880i | \(0.990994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.14796 | − | 1.98832i | −0.0385012 | − | 0.0666860i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.2763 | − | 16.5188i | 0.678521 | − | 0.552781i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.97090 | − | 13.8060i | 0.266438 | − | 0.461484i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.8580 | + | 34.3951i | 0.662302 | + | 1.14714i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.5485 | 1.05103 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.4012 | 1.57567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2567 | + | 17.7651i | −0.340569 | + | 0.589882i | −0.984538 | − | 0.175169i | \(-0.943953\pi\) |
0.643970 | + | 0.765051i | \(0.277286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9608 | −0.727594 | −0.363797 | − | 0.931478i | \(-0.618520\pi\) | ||||
−0.363797 | + | 0.931478i | \(0.618520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.4404 | −0.709572 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.06418 | + | 13.9676i | −0.266303 | + | 0.461250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0898 | −0.728674 | −0.364337 | − | 0.931267i | \(-0.618704\pi\) | ||||
−0.364337 | + | 0.931267i | \(0.618704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6459 | 0.383329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.5351 | + | 56.3524i | 1.06975 | + | 1.85286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.2645 | − | 45.4914i | 0.861709 | − | 1.49252i | −0.00856978 | − | 0.999963i | \(-0.502728\pi\) |
0.870278 | − | 0.492560i | \(-0.163939\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8675 | + | 67.3274i | 0.356169 | + | 2.20657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.3269 | + | 87.1687i | 1.64586 | + | 2.85072i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9688 | + | 22.4627i | 0.423674 | + | 0.733824i | 0.996296 | − | 0.0859953i | \(-0.0274070\pi\) |
−0.572622 | + | 0.819820i | \(0.694074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.90673 | + | 15.4269i | 0.290351 | + | 0.502903i | 0.973893 | − | 0.227009i | \(-0.0728946\pi\) |
−0.683542 | + | 0.729911i | \(0.739561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2216 | 0.430555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.0446 | + | 29.5221i | −0.553874 | + | 0.959339i | 0.444116 | + | 0.895969i | \(0.353518\pi\) |
−0.997990 | + | 0.0633691i | \(0.979815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.51754 | 0.146646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.34224 | + | 10.9851i | −0.205445 | + | 0.355842i | −0.950275 | − | 0.311413i | \(-0.899198\pi\) |
0.744829 | + | 0.667255i | \(0.232531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.5235 | + | 73.6529i | −1.37603 | + | 2.38335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.8384 | − | 75.9304i | −1.41562 | − | 2.45192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3108 | 0.751961 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.3191 | − | 80.2271i | −1.49107 | − | 2.58260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.6266 | − | 40.9225i | 0.759780 | − | 1.31598i | −0.183182 | − | 0.983079i | \(-0.558640\pi\) |
0.942962 | − | 0.332899i | \(-0.108027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6810 | + | 30.6244i | −0.567410 | + | 0.982782i | 0.429411 | + | 0.903109i | \(0.358721\pi\) |
−0.996821 | + | 0.0796733i | \(0.974612\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0466368 | − | 0.0807773i | −0.00149511 | − | 0.00258960i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.0660 | −1.44179 | −0.720895 | − | 0.693044i | \(-0.756269\pi\) | ||||
−0.720895 | + | 0.693044i | \(0.756269\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2858 | + | 31.6719i | 0.584417 | + | 1.01224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0915 | + | 22.6752i | −0.417555 | + | 0.723226i | −0.995693 | − | 0.0927130i | \(-0.970446\pi\) |
0.578138 | + | 0.815939i | \(0.303779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.5972 | − | 73.7805i | 1.35726 | − | 2.35084i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.85204 | −0.0906897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6070 | − | 18.3719i | 0.336942 | − | 0.583601i | −0.646914 | − | 0.762563i | \(-0.723941\pi\) |
0.983856 | + | 0.178962i | \(0.0572739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.3304 | 1.65898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.1364 | + | 47.0016i | 0.859418 | + | 1.48856i | 0.872485 | + | 0.488642i | \(0.162507\pi\) |
−0.0130661 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(998\) | 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 | 1368.2.s.j.505.1 | 6 | ||
3.2 | odd | 2 | 456.2.q.f.49.3 | ✓ | 6 | ||
4.3 | odd | 2 | 2736.2.s.x.1873.1 | 6 | |||
12.11 | even | 2 | 912.2.q.k.49.3 | 6 | |||
19.7 | even | 3 | inner | 1368.2.s.j.577.1 | 6 | ||
57.8 | even | 6 | 8664.2.a.z.1.1 | 3 | |||
57.11 | odd | 6 | 8664.2.a.x.1.1 | 3 | |||
57.26 | odd | 6 | 456.2.q.f.121.3 | yes | 6 | ||
76.7 | odd | 6 | 2736.2.s.x.577.1 | 6 | |||
228.83 | even | 6 | 912.2.q.k.577.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.q.f.49.3 | ✓ | 6 | 3.2 | odd | 2 | ||
456.2.q.f.121.3 | yes | 6 | 57.26 | odd | 6 | ||
912.2.q.k.49.3 | 6 | 12.11 | even | 2 | |||
912.2.q.k.577.3 | 6 | 228.83 | even | 6 | |||
1368.2.s.j.505.1 | 6 | 1.1 | even | 1 | trivial | ||
1368.2.s.j.577.1 | 6 | 19.7 | even | 3 | inner | ||
2736.2.s.x.577.1 | 6 | 76.7 | odd | 6 | |||
2736.2.s.x.1873.1 | 6 | 4.3 | odd | 2 | |||
8664.2.a.x.1.1 | 3 | 57.11 | odd | 6 | |||
8664.2.a.z.1.1 | 3 | 57.8 | even | 6 |